International Journal of Differential Equations
Volume 2012 (2012), Article ID 838947, 21 pages
http://dx.doi.org/10.1155/2012/838947
Research Article

Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence

R. K. Pandey and A. K. Barnwal

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India

Received 25 May 2012; Accepted 12 July 2012

Academic Editor: Yuji Liu

Copyright © 2012 R. K. Pandey and A. K. Barnwal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence of multiple nonnegative solutions for the doubly singular three-point boundary value problem with derivative dependent data function − ( 𝑝 ( 𝑡 ) 𝑦 ′ ( 𝑡 ) ) ′ = 𝑞 ( 𝑡 ) 𝑓 ( 𝑡 , 𝑦 ( 𝑡 ) , 𝑝 ( 𝑡 ) 𝑦 ′ ( 𝑡 ) ) , 0 < 𝑡 < 1 , 𝑦 ( 0 ) = 0 , 𝑦 ( 1 ) = 𝛼 1 𝑦 ( 𝜂 ) . Here, 𝑝 ∈ 𝐶 [ 0 , 1 ] ∩ 𝐶 1 ( 0 , 1 ] with 𝑝 ( 𝑡 ) > 0 on ( 0 , 1 ] and 𝑞 ( 𝑡 ) is allowed to be discontinuous at 𝑡 = 0 . The fixed point theory in a cone is applied to achieve new and more general results for existence of multiple nonnegative solutions of the problem. The results are illustrated through examples.