MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH MIXED NONLINEARITY

This article concerns the fourth-order elliptic equation Delta(2)u - Delta u + lambda V(x)u - f(x, u) + mu xi(x)vertical bar u vertical bar(p-2)u, x is an element of R-N u is an element of H-2 (R-N) where lambda > 0 is a parameter, V is an element of C(R-N, R) and V-1(0) has nonempty interior. Under some mild assumptions, we establish the existence of two nontrivial solutions. Moreover, the concentration of these solutions is explored on the set V-1(0) as lambda -> infinity. As an application, we give the similar results and concentration phenomenona for the above problem with concave and convex non linearit ies.