EXISTENCE OF SOLUTIONS AND BIFURCATION OF A CLASS OF FIRST-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

SHI BAO, LI ZHIXIANG

Acta Mathematicae Applicatae Sinica ›› 1995, Vol. 18 ›› Issue (1) : 83-89.

中国科学院数学与系统科学研究院期刊网
Acta Mathematicae Applicatae Sinica ›› 1995, Vol. 18 ›› Issue (1) : 83-89. DOI: 10.12387/C1995010

EXISTENCE OF SOLUTIONS AND BIFURCATION OF A CLASS OF FIRST-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

  • SHI BAO1, LI ZHIXIANG2
Author information +
History +

Abstract

In this paper,the behaviour of solutions of the Equation:
x'(t)=(x2(t)-μ)x(x(t))μ≤0(1)
are studied.Some new results as well se similar ones to Eder[1],Wang[2] and the suthor[3] are obtained as μ<0.The existence of strictly monotone maximal strong solutions which can not be continuated to ∞ in the two ends are proved as μ=0,i.e.,μ=0 is a bifurcation value of the above Equation.

Key words

FLnctional differential equations / state-dependent deviation arguments / strong solutions / maximal strong solutions / bifurcation

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations
SHI BAO, LI ZHIXIANG. EXISTENCE OF SOLUTIONS AND BIFURCATION OF A CLASS OF FIRST-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS. Acta Mathematicae Applicatae Sinica, 1995, 18(1): 83-89 https://doi.org/10.12387/C1995010

References

1 Eder,E.,The Function-Differential Equations x'(t)=x(x(t)),J.Diff.Equs,1984,54:390-400.
2 Wang,K(王克),On the Equation x'(t)=f(x(x(t))),Funk.Ekv.,1990,33:405-425.
3 时宝,关于泛函微分方程,国防科技大学学报,1993,15 (2): 84-88.
4 郑祖麻,关于泛函微分方程的发展和应用,数学进展,1983,12 (2):94-112.
5 郑祖麻,非R.N.A.型泛函微分方程的近期进展,安徽大学学报(自然科学版),1994,(1): 11-31.
6 Hsing,D-P,K.,Existence and Uniqueness Theorem for the One-Dimensional Backwards Two-Body Problem of Electrodynamics,Phya.Rev.,1977,D16 (4): 974-982.
7 Driver,R.D.,Can the Future Influence the Present? Phys.Rev,1079,D19(4):1098-1107.
8 吴汉忠,方程解的存在性及其渐近性态,安徽大学硕士学位论文,1990.
9 时宝,常微分方程与泛函微分方程德定性分析,国防科技大学研究生院硕士学位论文,1993.
10 Shi,B(时宝)&Li,Z.X.(李志祥),On a New Type of Functional Differebtial Equations,three Internet.Conf.on Diff.Equations,Springer-Verlag,New York,second edition,1993.
11 Hale,J.K.,Theory of Functional Differentiall Equations,Springer-Verlag,New York,second edition,1993.

136

Accesses

0

Citation

Detail
Sections
Recommended

/

〈 〉