Ground state solutions and concentration phenomena in nonlinear eigenvalue problems with variable exponents

Abstract

  In this paper we consider a class of nonlinear eigenvalue problems that involves a particular nonhomogeneous operator with variable growth condition and multiple variable exponents. The main results establish the existence of minimum action solutions and the concentration of the spectrum in a bounded interval.

  The proofs rely on variational arguments based on the Mountain-Pass Theorem and the Nehari manifold technique.