Abstract By using a perturbation result on the ranges of maximal monotone operators, and by using a method of constructing an auxiliary nonlinear equation, a nonlinear parabolic equation involving the generalized p-Laplacian operator with mixed boundary conditions is studied in this paper. An abstract result of the existence of solution for this nonlinear bound-ary value problem is obtained. The method used in this paper extends and complements some of the previous work.

In linear topological space, by the aid of the alternative theorem of intcone-convexlikeness, the Lagrange type optimality condition for the set-valued optimization problem with constraints is obtained. The sufficient and necessary conditions of the problem is also established. Then by applying separation theorem for convex sets, the Kuhn-Tucker optimality condition is given, and meanwhile the corresponding sufficient condition and the corresponding sufficient and necessary conditions is also obtained.

In this paper,we consider a class of periodic discrete nonlinear Schrödinger systems. Under a weaker superlinear condition than the classical Ambrosetti-Rabinowitz condition, by using the generalized Nehari manifold approach developed by Szulkin and Weth, we prove the existence of standing wave solutions for discrete Schrödinger systems, the results generalize the corresponding work of known literature. The same method can also be applied to obtain solutions for single discrete nonlinear Schrödinger equation.

This paper proposes confidence regions for the trend parameters in a linear polynomial regression model with long memory errors. This is a problem related to multi-dimensional space. We establish two kinds of confidence regions for the trend parameters based on the Ordinary Least Square Estimates (OLS) and the Generalized Least Squares Estimates (GLS). Then, we construct a calibrated confidence region, based on the concept of effective sample sizes. We measure the loss by the relative efficiency. Through a Monte Carlo simulation study, we do a comparison among the three methods of confidence regions in empirical coverage probabilities and the volume. The result shows that the advantages of our calibrated confidence regions lie in its good performance and easy computation.

A conforming finite element and a nonconforming finite element schemes of Possion equations are persented based on a new mixed variational form, then the weak coercivity of this form is established. Furthermore, through integral identity techniques the superclose properties of the related variables are derived under anisotropic meshes. At the same time, the global superconvergence is obtained by constructing the interpolation post-processing operator. In contrast to other mixed finite element schemes, new schemes have some advantages: the B-B condition is easy to be proved; fewer degrees of freedom is involved and the lowest order conforming rectangle element is the simplest rectangle element so far; one order higher convergence results than that of the conventional analysis can be derived.

It offers the stochastic asymptotic stability on SVIE and the properties of the limit sets of solutions of SVIE via multiple Lyapunov functions.Moreover, we obtain a series of methods for determining the stochastic stability, which enable us to construct the Lyapunov functions much more easily in applications.

This paper is concerned with a class of planar differential system of nine degrees.By making two appropriate transformations of system and calculating focal values carefully, we obtain the conditions that the infinity and five elementary foci (-1/2,0),(-1/2,±√3/2) (±1/2/, -√3/6) become six general centers at the same time.Moreover 12 limit cycles including 10 small limit cycles from five elementary foci and 2 large limit cycles from the infinity can occur at the same step of disturbance under a certain condition.What is worth mentioning is that similar conclusions have hardly been seen in published paper up till now and our work is significative.

In order to derive the existence of solution of quasi-variational inequality for functions with no continuity defined on abstract convex spaces with no linear structure. Firstly, by using KKM theorem in abstract convex space, the existence of solutions of Ky Fan inequality is proved. By the way, the existence of solutions of weakly quasi-variational inequality and quasi-variational inequality is derived. Furthermore, the Fan-Glicksberg-Kakutani fixed point theory, Kakutani fixed point theory and Tycholoff fixed point theory in abstract convex space, as corollaries, are derived. As an application, the existence of Nash equilibrium for n-person non-cooperative generalised game on abstract convex strategy spaces is established.

The Conditional Poisson Sampling for selecting sample with fixed size n is an approximate πPS sampling design without replacement. Many unequal probability sampling designs are developed or improved based on the Conditional Poisson Sampling or the Poisson Sampling. In the traditional theory of unequal probability sampling design, the knowledge of the first-order inclusion probabilities π_i and the second-order inclusion probabilities π_ij are needed to build the unbiased estimator of Horvitz-Thompson for the population total or mean of study variable Y and to obtain variance estimation of this estimator. Previous studies indicated it is necessary to use the formula of the first-order inclusion probabilities for the Conditional Poisson Sampling to calculate the inclusion probabilities for other designs. However, topics in developing recursive formulas of the inclusion probabilities for the Conditional Poisson Sampling have not been well investigated. This paper aims at improving recursive formulas of the first-order inclusion probabilities for the Conditional Poisson Sampling and broadening its applicable range. Remarkably, this paper presents the recursive formula of the second-order inclusion probabilities at the first time. Examples in the paper illustrate the availability of the proposed recursive formula. The obtained results significantly improve the theory of the Conditional Poisson Sampling, and exhibit potential application value.

This paper studies a kind of exploration problem with N vehicles, by modeling, the author transforms the N vehicles exploration problem to a sequential decision problem with an exponential computational time complexity of O(n!). In particular, the author embeds the problem within a dynamic programming framework, and introduces two types of heuristic algorithms. Based on which, the author proposes a kind of rollout algorithm which is related to notions of policy iteration, and improves the performance of the base heuristic algorithm by costing a reasonable time complexity. Numerical examples are stated at last.

Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the growth of solutions of a class of higher-order nonlinear algebraic differential equation, and obtain one result which due to Gao Lingyun et al is in proved and generalized.

In real Hilbert spaces, the algorithm for solving the split common fixed point problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudocontractive mapping is studied. Under suitable conditions the weak convergence and the strong convergence of the sequence are proved. The results extend and improve the corresponding results announced by many others.

Let {X_k, k≥1} be a d-variate Gaussian vector sequence with X_k=(X_k1…, X_kd). Denote its partial maxima and minima respectively by M(n)=(M_n1,…,M_nd) and m(n)=(m_n1,…,m_nd), where M_ni=max{X_ki, 1≤k≤n}, m_ni=min {X_ki, 1≤k≤n}. The joint limiting distribution and joint version of the almost sure convergence for the maxima and minima are derived under some conditions, respectively.

This paper deals with the multiplicity of solutions for some fractional elliptic equation (-Δ)^su=λf(x,u) under Dirichlet boundary condition. By using the asymptotic behavior of the nonlinearity f at zero and infinity without Ambrosetti-Rabinowitz growth condition, we apply mountain pass theorem and suitable truncation to obtain the existence of one positive solution and one negative solution for all the parameter lambda λ >0.

It is readily observed that the habitat of many biological species often undergoes some periodic changes because of the such effects as seasoning variations. On the other side, lots of ecological studies show that the vital parameters of an individual are closely connected with its body size, such as mass, length, surface area, volume, etc. Motivated by these considerations, we in this paper investigate an exploitation problem of renewable biological resources incorporating the individual's size-structure and periodical changes into the population model. Firstly we propose an integro-partial system to describe the population dynamics, in which the mortality, fertility, growth rate and harvesting effort are time-periodic functions and the boundary condition (i.e. renewal equation) is of global feedback form. Then we treat the well-posedness problem of the state system. By means of characteristics an integral equation is established for the population fertility, which is put into an abstract framework in a suitable space of functions. Roughly speaking, the model will be well posed if the reproducing number is less than one. Secondly we prove the existence of optimal policies via a maximizing sequence and a use of Mazur's theorem in convex analysis. Following that is a careful derivation of necessary optimality conditions, which is finished by tangent-normal cones and adjoint system techniques, and provide an exact description for the optimal strategies. Excluding the singular cases enable us to assert that optimal controllers are unique and take the form of bang-bang, but we cannot expect an explicit formula for them due to complexities. Finally, we present an algorithm to compute the optimal group and test it with an example.

We present a new projection method for solving quasi-variational inequalities. This new method consists of following two steps: First, we construct a hyperplane which can separate strictly current iterate from the solution set of the quasi-variational inequalities. Second, the next iterate is generated by projecting the current iterate onto the intersection of the feasible set C and this hyperplane. Our method is proven to be globally convergent under certain assumptions. Nnumerical experiments show that our method have the less total number of iterative steps.

In this paper, we consider the eigenvalue and the inverse eigenvalue problem of the Dirac operator defined on [0,1], which has the jump conditions on t₀in (0,1) and two Dirac operators defined respectively on subset [0,t₀] and [t₀,1], by using the monotonicity of the Weyl-Titchmarsh-m-function, the alternation of the three spectra is considered, we prove that the pair of potentials (p(x),r(x) and the parameter h,H in the boundary conditions can be uniquely determined by the three spectra if the two spectra of the operators defined on subsets are disjoint.

In this paper, a new generalized projection feasible algorithm is proposed for solving the nonlinear inequality constrained optimization. A new projection direction is proposed. We don't compute an ε active set, so the computational cost is reduced. The theoretical analysis shows that the algorithm is global and superlinear convergence under some suitable conditions.

In this paper, an optimal portfolio strategy is characterized under Knightian uncertainty and partial information. We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. For the Knightian uncertainty investor's objective of maximizing the α-maxmin expected utility of the terminal wealth, by using HMM filtering theory and Malliavin calculus we derive an explicit representation of the optimal trading strategy. A feature of our model is that it adopts the α-maxmin expected utility which is differentiating ambiguity and ambiguity attitude. And from the explicit solution of optimal portfolio strategy we know that ambiguity and ambiguity attitude can significantly affect the behavior of investors. Thus the conclusion of this paper has an economic significance.

This paper considers the sensitivity of defective multiple eigenvalues of a quadratic matrix polynomial problem dependent on several parameters. The average of eigenvalues is proved to be analytic, the derivatives of the average eigenvalues and the corresponding eigenvector matrices are obtained. The results are useful for investigating structural optimal design, model updating, and structural damage detection.

The single-index model is an important tool in multivariate nonparametric regression. It not only can reduce the dimension of data, but also can capture the main feature of data. This paper deals with M-estimators for the partial linear single-index model. A two-step estimates procedure based on local linear polynomial approximation is proposed.Under some mild regular conditions, the asymptotic properties of the proposed M-estimators of unknown function and its derivative and the M-estimator of parameter is investigated. The finite sample properties of the estimation is considered by a random simulation study.

In this paper, by using the fixed point index theory and lower and upper solutions method, we are concerned with the existence, multiplicity and nonexistence of positive periodic solutions for a kind of functional differential equation. The existence, multiplicity and nonexistence results are established in terms of different value of parameters.

In this paper we establish an estimation procedure of the varying-coefficient mixed model and study the asymptotic normality of the estimation. Firstly, we eliminate the random effects by an orthogonality matrix. Then using the local linear method, we obtain an orthogonality-based estimation (OBE) of the functional coefficient and prove that it is asymptotically normal. Since the random effects are eliminated, the OBE estimation is not efficient. By the ordinary consistent estimations of covariance of error and random effects, we propose an iterate process to modify it. With the same method we can prove this modified estimation is also asymptotically normal.

We consider the Cauchy problem of a coupled Navier-Stokes-Nernst-Planck-Poisson system modeling the flow of electro-hydrodynamics, and show the global existence of unique strong solution in 2D for general large initial data and in 3D for small initial data. The time decay rates of the weak solutions in 3D is also obtained.

This paper studies a class of stochastic linear complementarity problems (SLCPs) with finitely many realizations. By making use of the Fischer-Burmeister (FB) and min functions, this class of SLCPs is formulated as a constrained minimization problem. Then, a feasible projected Barzilai-Borwein (BB) gradient method is applied for solving the constrained minimization problem. Preliminary numerical results show that the formulation can yield a solution with high safety and less value of the optimality function for SLCPs.

Let G=(V，E) be a graph with sets of vertices and edges V and E, respectively. A total k-coloring of G is a mapping φ: V∪E→{1,2,…,k} such that φ(x)≠φ(y) whenever x and y are two adjacent or incident elements of V∪E. G is totally k-colorable if it admits a total k-coloring. In this paper, we use discharging method to prove that plane graphs with maximum degree 7 and without chordal 7-cycle are totally 8-colorable. This improves some known results on this topic of totally 8-colorability of plane graphs with maximum degree 7.

We investigate some coupled KdV equations, by means of prolongation structure theory. We discuss their prolongation Lie algebra. The Lax pairs of the corresponding systems are derived theoretically.

The improved Kyle model under the incomplete information with a risk-seeking insider trader, which is an insider trading model and a dynamic game model, was studied. The incomplete information means that, the insider trader only knows a signal of the fundamental value of a risky asset but not it. The unique equilibrium of this model was determined, the asymptotic behavior of some financial variables in the model was analyized, and the economic meaning of variation feature for these variables was also given.

To investigate the uniqueness and existence of viscosity solutions of Hamilton-Jacobi equations in the time pseudo almost periodic case, this paper use the comparison theorem of Hamilton-Jacobi equations and the property of the pseudo almost periodic functions to get such results.

Based on rounded data, the empirical Bayes one-sided test problem for the parameter of a class of exponential distributions is investigated. The empirical Bayes test rule is constructed. It is shown that the asymptotically optimal property and convergence rate for the proposed EB test rule are obtained under suitable conditions. Finally, an example about the main result of this paper is given.

In this paper, we concern the existence of solutions of a class of semilinear elliptic system with nonlinear boundary conditions. We prove that the system has at least two nontrivial nonnegative solutions by Nehari manifold method, and then using strong maximum principle, show the positivity of these solutions.

A class of periodic reaction-diffusion population model with age-structure and dispersal kernel is discussed in the paper. Via study on the spatial dynamics to the relative delay differential equations, we prove the the system admits an unique positive periodic solution, which is also globally asymptotically stable. By appealing to the theory of monotonic periodic semiflows, we establish the traveling wave solution and spreading speed c^* with the periodic reaction-diffusion population model. That is, continuous periodic traveling wave exists when wave speed c>c^*, and nonsexists when c<c^*.

Motivated by Filippov set-valued mapping and theory of nonsmooth analysis, adaptive L₂-gain controller design approach is proposed for systems of time-delay differential equations with nonsmooth right-hand sides. By chain rule for Lyapunov-Krasovkii functional and a result about the relation between L₂-gain and stability, an adaptive L₂-gain controller is derived. Under certain conditions, it is proven that the nonsmooth system is controllable and the control law guarantees the close-loop system disturbance attenuation with internal stability in the sense of Filippov solutions.

Among the methods with cell-centered unknowns on large distortion meshes, most adopt the vertex unknowns directly or indirectly, and the accuracy of some methods such as the nine-point scheme is ultimately determined by the approximation to the vertex unknowns. In this paper, taking advantage of the high-order accuracy of the "twin-fitting" method especially on discontinuous diffusion coefficients, a new treatment for the vertex unknowns is developed to apply to a nine-point scheme. Numerical experiments show that the new nine-point scheme has almost second order accuracy on distorted meshes and on discontinuous diffusion coefficients.

In this paper, we consider the elliptic p-Laplace equation with nonlinear source and its perturbation -div(|∇u|^p-2∇u)=u^q+f(x,t,u,∇u), where p>2 and q>p-1. For this problem we prove an a priori estimates for both nonnegative solution and its gradient. Also we get the similar estimates of nonnegative solutions for the elliptic systems consisting of two equations. We mainly depend on the Doubling lemma and some known Louville-type theorems for elliptic equations and systems.

A model of constraint satisfaction problem with growing domains, called Model RA, is investigated in this paper. It is discovered that when constraint density is small (for example, when density parameter is 25% of the satisfiability phase transition point), backtrack-free algorithm can solve Model RA with probability tending to 1, and the solving time is polynomial.

A two order wave equation of kdv type, a typical nonlinear wave equation, has broad application prospect. With the canonical momenta, two new multi-symplectic formulations for the two order wave equation of KdV type are presented, and the associated local conservation laws are shown. A two order wave equation of kdv type was sdudied based on the multi-symplectic theory in Hamilton space.The multi-symplectic formulations of a two order wave equation of kdv type with several conservation laws are presented. The symplectic Preissmann method is used to discretize the formulations. The numerical experiment is given, and the results verify the efficiency of the multi-symplectic scheme.

The asymptotic solutions of a initial value problem about a class of differential difference equations with two small delays are studied. Here, two small delays are small parameters of different orders of magnitude. A power series expansion consisting of the outer solution and the boundary layer of the initial value problem are constructed firstly under the certain conditions. Then the outer solution is given by the degenerate form of the original problem. Finally by various stretched variables, according to the nature of the boundary layers, the boundary layers of two orders of magnitude of the initial value problem are given respectively. So, the asymptotic solutions of two cases are obtained. The boundary layers are both found staircase structure.

In this paper, by applying the concept of absolute stability about the certain variable, the necessary and sufficient conditions of absolute stability are obtained, which are about general discrete Lurie systems with superposition of nonlinearities. In virtue of discrete gronwall inequality, some sufficient conditions is also obtained. A numerical example illustrates the effectiveness of the results.

A new penalty-free primal-dual interior-point algorithm is proposed in this paper. Rather than the exact penalty function and the filter, the presented framework guarantees global convergence by controlling the infeasibility of iterates. At each iteration, the algorithm obtains a search direction by solving a linear system. Then a backtracking line search is performed with certain aim depending on comparison between the measures of current optimality and feasibility to determine the step length. No feasible restoration phase is needed. Global convergence is proved under suitable assumption. Preliminary numerical results are reported.