SCHRODINGER EQUATIONS IN R4 INVOLVING THE BIHARMONIC OPERATOR WITH CRITICAL EXPONENTIAL GROWTH

In this paper we prove the existence of at least one nontrivial ground state solution for fourth-order elliptic equations of the form (P) Delta(2)u -Delta u + u =K(x)[f(u) + g(u)], x epsilon R-4, u epsilon H-2(R-4), where Delta(2)u := Delta(Delta) is the biharmonic operator, f is a continuous nonnegative function with polynomial growth at infinity, g is a continuous nonnegative function with exponential growth and K is a positive bounded continuous function that can vanish at infinity. Our results complete the analysis made in F. Sani (Comm. Pure Appl. Anal. 12 (2013), 405-428), where the author studied Schrodinger equations involving the biharmonic operator with coercive potentials. Our approach is based on various techniques such as the mountain-pass theorem, Trundinger-Moser type inequalities and compactness results.