Multiple positive solutions for singular multi-point boundary-value problem with general growth on the positive half line

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.

Keywords

• Fixed point
• multiple solutions
• multi-point
• singularity
• infinite interval
• cone