On a weighted Adams type inequality and an application to a biharmonic equation

Abstract

This paper deals with an improvement of a class of Adams type inequalities involving potentials and weights , which can decay to zero at infinity as , , and , , respectively. As an application of this result and by using minimax methods, we establish the existence of solutions for the following class of problems: where the nonlinear term can have critical exponential growth. Furthermore, when we prove that the solutions belong to the Sobolev space (bound state solutions).