Morse indices at critical points related to the symmetric mountain pass theorem and applications

Abstract

We obtain estimates of Morse indices of an even functional at critical points related to the Symmetric Mountain Pass Theorem ([AR, R1, R4]). As applications, we deal with the existence of multiple solutions of inhomogeneous super linear boundary value problems and improve the result of [BB1, St, R2, BL]. We also deal with superlinear Sturm—Liouville problem: in (0,1) and give a complete characterization of the solutions related to the Symmetric Mountain Pass Theorem