Three positive solutions for a generalized Laplacian boundary value problem with a parameter

摘要

Concerned is a generalized Laplacian boundary value problem with a positive parameter. First we apply the Leggett–Williams fixed point theorem to establish sufficient conditions on the existence of at least three positive solutions for the parameter belonging to an explicit interval. Then, under a little bit stronger assumptions, we show that there are at least three positive symmetric solutions for the parameter in an open interval. The obtained results are new even for Laplacian boundary value problems and they are illustrated with an example.