The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Wei, Yuming^1,2  Wong, Patricia J. Y.³  Ge, Weigao¹ 

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] Guangxi Normal Univ, Sch Math Sci, Guilin 541004, Peoples R China

[3] Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore

关键词: Boundary value problems;    Positive solutions;    Delay differential equations;    Infinite interval;   

DOI  :  10.1016/j.cam.2009.10.005

来源: Elsevier

【 摘 要 】

In this paper, we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval (phi(x'(t)))' + a(t)f(t, x(t), x(t)) = 0, 0 < t < infinity, x(0) = xi, lim(t ->infinity) x'(t) = 0, where phi : R -> R is an increasing homeomorphism and a positive homomorphism with phi(0) = 0, x(t) is a function in C([-r, 0], R) defined by x(t) (sigma) = x(t+sigma) for -r <= sigma <= 0, and xi is an element of C([-r, 0], R). By using the fixed-point index theory and a new fixed-point theorem in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. The conclusions in this paper essentially extend and improve the known results. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

【 授权许可】

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