Existence and multiplicity results for Singular phi-Laplacian BVPs on the positive half-line

Abstract

This work proves the existence and multiplicity of positive solutions for a second-order nonlinear three-point phi-Laplacian boundary-value problem posed on the positive half-line. The nonlinearity depends on the solution and its derivative and may exhibit a time singularity at the origin. Existence of single and multiple nontrivial positive solutions is proved using fixed point index theory.

Keywords

• phi-Laplacian
• three point BVPs
• positive solutions
• singularity
• fixed point in a cone