Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrodinger equations

Abstract

We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schrodinger equations. Actually, using the classical Mountain Pass Theorem and minimization techniques, we prove the existence of critical points of the associated functional constrained on the Nehari manifold. Furthermore, we show that using the so-called fibering method and the Lusternik-Schnirerman theory there exist infinitely many solutions, actually a countable family of critical points, for such a semilinear bi-harmonic Schrodinger system under study in this work.