Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 32, pp. 1-29.
Title: Multiple positive solutions for singular multi-point
boundary-value problem with general growth on the positive half line
Authors: Smail Djebali (E.K.S., Algiers, Algeria)
Karima Mebarki (A.E. Mira Univ., Bejaia, Algeria)
Abstract:
This work is devoted to the existence of nontrivial positive
solutions for a class of second-order nonlinear multi-point
boundary-value problems on the positive half-line. The novelty of
this work is that the nonlinearity may exhibit a singularity at
the origin simultaneously with respect to the solution and its
derivative; moreover it satisfies quite general growth conditions
far from the origin, including polynomial growth. New existence
results of single, twin and triple solutions are proved using the
fixed point index theory on appropriate cones in weighted Banach
spaces together with two-functional and three-functional fixed
point theorems. The singularity is treated by means of
approximation and compactness arguments. The proofs of the
existence results rely heavily on several sharp estimates and
useful properties of the corresponding Green's function.
Submitted August 26, 2010. Published February 23, 2011.
Math Subject Classifications: 34B15, 34B16, 34B18, 34B40.
Key Words: Fixed point; multiple solutions; multi-point; singularity;
infinite interval; cone.