Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations. (June 2015)

• Record Type: Journal Article
• Authors: Álvarez-Caudevilla, P.; Colorado, E.; Galaktionov, V.A.
• Is Part Of: Nonlinear analysis. Volume 23(2015)
• Page Start: 78
• Page End: 93
• Publication Date: 2015-06
• Subjects: Nonlinear bi-harmonic Schrödinger equations -- Standing waves -- Critical point theory; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.11.009
• Languages: English
• ISSNs: 1468-1218

Abstract

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.