Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations. (June 2015) - Álvarez-Caudevilla, P.; Colorado, E.; Galaktionov, V.A.
Abstract: We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schrödinger 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–Schnirel'man theory there exist infinitely many solutions, actually a countable family of critical points, for such a semilinear bi-harmonic Schrödinger system under study in this work.