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

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 \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 Schrödinger system under study in this work.