Ordered solutions for degenerate Kirchhoff problems

Abstract

In the present paper we study a parametrized Kirchhoff type equation with two degeneracy points. The existence of two -norm ordered solutions is established for small value of the parameter via a careful analysis of the fiber maps associated to the energy functional. As a consequence we show existence of multiple or even infinitely many solutions to degenerate Kirchhoff equations. Due to the simplicity of the conditions, many applications are given.