Multiplicity of positive solutions for singular three-point boundary value problems at resonance

Abstract

In this paper, we study the existence and multiplicity of positive solutions for the three-point boundary value problems with singular nonlinear perturbations at resonance. The existence results are applicable to both the case of a strong singularity and the case of a weak singularity. The proof is based on a nonlinear alternative Leray–Schauder principle and a fixed point theorem in cones for completely continuous operators.