Ground State Solutions for a Class of Problems Involving Perturbed for the Biharmonic Operator with Non-local Term

In this paper, we study the existence of ground state solutions for an equation that involves a perturbation of a biharmonic operator with a non-local term. More precisely, we study the equation Lu = tau f(x,u) + beta|u|(2 & lowast;& lowast;-2)u in Omega and u = partial derivative u/partial derivative eta = 0 on partial derivative Omega where Omega subset of R(N )is a bounded smooth domain, L(<middle dot>) it is the biharmonic operator perturbed by the non-local operator that we will later define, tau > 0; here, 2(& lowast;& lowast; )= 2N/N-4 with N >= 5. We show the existence of a ground state solution using variational methods considering the subcritical case, i.e., beta=0 and the critical case, i.e., beta=1.