The existence of multiple positive solutions for singular functional differential equations with sign-changing nonlinearity

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Zhao, Yulin¹  Chen, Haibo² 

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412008, Peoples R China

[2] Cent S Univ, Dept Math, Changsha 410075, Hunan, Peoples R China

关键词: Functional differential equation;    Boundary value problem;    Multiple solutions;    Sign-changing;    Singular;   

DOI  :  10.1016/j.cam.2010.02.034

来源: Elsevier

【 摘 要 】

In this paper, we study the existence of multiple positive solutions for boundary value problems based on second-order functional differential equations with the form {y (t) + f (t, y(t - tau)) = 0, for all t is an element of (0, 1)\{tau}, y(t) = eta(t), for all t is an element of [-tau, 0], y(1) = 0 where 0 < tau < 1 and f : (0, 1) x (0, +infinity) > (-infinity , +infinity) is continuous, may be singular at t = 0, 1,y = 0 and takes negative values. By applying the fixed point index theorem, we obtain the conditions for the existence of at least two and of three positive solutions. An example to illustrate our results is given. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free