Existence of solutions for a system of coupled nonlinear stationary   bi-harmonic Schr\"{o}dinger equations
  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. 
P. \'Alvarez-Caudevilla, E. Colorado, V. A. Galaktionov
math.AP