Positive solutions for second-order multi-point boundary-value problems at resonance in Banach spaces.
Values of are determined for which there exist positive solutions of the system of three-point boundary value problems, , , for , and satisfying, , , , . A Guo-Krasnosel’skii fixed point theorem is applied.
We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.