一类变指数基尔霍夫型方程的无穷多解

张申贵

应用数学学报 ›› 2018, Vol. 41 ›› Issue (6) : 801-810.

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应用数学学报 ›› 2018, Vol. 41 ›› Issue (6) : 801-810. DOI: 10.12387/C2018062
论文

一类变指数基尔霍夫型方程的无穷多解

    张申贵
作者信息 +

Infinitely Many Solutions for a Class of Kirchhoff-type Equation with Variable Exponent

    ZHANG Shengui
Author information +
文章历史 +

摘要

本文研究带有各向异性p（x）-Laplace算子的基尔霍夫型方程Dirichlet边值问题

其中Ω是RN（N ≥ 3）中具有光滑边界的有界区域，f（x，u）∈C（Ω×R，R），∂xi u=∂u/∂xi，i=1，2，…，N，且Mi（t）：R+→R+，H（t）：R→R和pi（x）：Ω→R为连续函数.当非线性项在零点附近次线性:增长时，运用临界点理论中的Clark定理获得了新的多重解存在性结果.

Abstract

In this paper, we investigate the following Dirichlet boundary value problem for Kirchhoff-type equation involving the anisotropic p(x)-Laplacian operator


where Ω⊂ RN (N ≥ 3)is a bounded domain with smooth boundary, f(x, u) ∈ C(Ω×R, R), ∂xiu=∂u/∂xi, i=1, 2, …, N, Mi(t):R+ → R+, H(t):R → R and pi(x):Ω → R are continuous functions. When the nonlinearity has a sublinear growth near zero, some new results for existence of multiplicity of solutions are obtained by using the Clark's theorem in critical point theory.

关键词

基尔霍夫型方程 / Dirichlet边值问题 / 各向异性p(x)-Laplace算子 / 临界点理论

Key words

kirchhoff-type equation / Dirichlet boundary value problem / anisotropic p(x)-Laplacian operator / critical point

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张申贵. 一类变指数基尔霍夫型方程的无穷多解. 应用数学学报, 2018, 41(6): 801-810 https://doi.org/10.12387/C2018062
ZHANG Shengui. Infinitely Many Solutions for a Class of Kirchhoff-type Equation with Variable Exponent. Acta Mathematicae Applicatae Sinica, 2018, 41(6): 801-810 https://doi.org/10.12387/C2018062

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基金

国家自然科学基金（31260098）和中央高校基本科研业务费专项基金（31920180041）资助项目.

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