Existence and Concentration of Solutions for a 1-Biharmonic Choquard Equation with Steep Potential Well in RN

In this paper, we investigate the existence and concentration of solutions for the following 1-biharmonic Choquard equation with steep potential well {Delta(2)(1) - Delta(1)u + (1 + lambda V (x)) u/vertical bar u vertical bar = (I-mu * F(u)) f (u) in R-N, u is an element of BL(R-N), where N >= 3, lambda > 0 is a positive parameter, V : R-N -> R, f : R -> R are continuous functions verifying further conditions, Omega = int(V-1({0})) has nonempty interior and I mu : R-N -> R is the Riesz potential of order mu is an element of (N -1, N), For lambda > 0 large enough, we prove the existence of a nontrivial solution u(lambda) of the problem above via variational methods and the concentration behavior of u(lambda) which is explored on the set Omega.