On weighted Adams type inequalities and applications

Abstract

This work deals with some classes of Adams-type inequalities involving potentials and weights that can decay to zero at in nity. From these inequalities, we establish compactness results and concentration-compactness results. As applications of these weighted Adams inequalities, using minimax methods, we prove the existence of solutions to some classes of elliptic problems involving the biharmonic operator on R4 and the polyharmonic operator on R2m; where the nonlinear term has critical exponential growth in the Trudinger-Moser sense. Furthermore, in some cases we prove that the solutions obtained are bounded in L2, which are the so-called bound state solutions.