Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity

Abstract

In this paper, we establish the existence of a ground state solution for a weighted fourth-order equation of Shrödinger type under boundary Dirichlet condition in the unit ball B of ℝ⁴. The potential V is a continuous positive function bounded away from zero in B. The nonlinearity of the equation is assumed to have exponential growth due to Adams-type inequalities combined with polynomial term. We use the constrained minimization in the Nehari set, the quantitative deformation lemma, and degree theory results.