Infinitely many solutions for $2k$-th order BVP with parameters

Abstract

In this paper we consider a special case of BVP for higher-order ODE, where, the linear part consists of only even-order derivatives and depends on a set of real parameters. Among many questions related to this problem we are especially interested in the specific one, namely to work out assumptions which provide existence of infinitely many solutions. This task is dealt with by applying a combination of both topological and variational methods, including Chang’s version of the Morse theory in particular.