The existence of countably many positive solutions for nonlinear singular m-point boundary value problems on the half-line

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:222

Article

Liang, Sihua^1,2  Zhang, Jihui¹ 

[1] Nanjing Normal Univ, Sch Math & Comp Sci, Inst Math, Nanjing 210097, Jiangsu, Peoples R China

[2] Changchun Normal Univ, Coll Math, Changchun 130032, Peoples R China

关键词: Sigularity;    Multiple positive solutions;    Boundary value problems;    Fixed-point theorem;    Half-line;    Cone;   

DOI  :  10.1016/j.cam.2007.10.062

来源: Elsevier

【 摘 要 】

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we study the existence of countably many positive solutions for nonlinear boundary value problems on the half-line (phi(u '))' + a(t) f (u(t)) = 0, 0 < t < +infinity. u(0) = Sigma(m-2)(i=1) alpha(i)u(xi(i)). u '(infinity) = 0. where phi : R -> R is the increasing hemeomorphism and positive homomorphism and phi(0) = 0. We show the sufficient conditons for the existence of countably many positive solutions by using the fixed-point index theory and a new fixed-point theorem in cones. (c) 2008 Published by Elsevier B.V.

【 授权许可】

Free