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arXiv · 1402.4165

Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schr\"{o}dinger equations

P. Álvarez-Caudevilla·E. Colorado·V. A. Galaktionov
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Abstract

We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schr\"{o}dinger 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 \emph{Nehari manifold}. Furthermore, we show that using the so-called \emph{fibering method} and the \emph{Lusternik-Schnirel'man theory} there exist infinitely many solutions, actually a countable family of critical points, for such a semiliner bi-hamonic Schr\"{o}dinger system under study in this work.

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P. Álvarez-Caudevilla, E. Colorado, V. A. Galaktionov. 2014-02-17. Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schr\"{o}dinger equations. https://arxiv.org/abs/1402.4165

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