MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR NONLINEAR FRACTIONAL ELLIPTIC EQUATIONS WITH STEEP POTENTIAL

In this article, we prove the existence, multiplicity and concentration of non-trivial solutions for the following indefinite fractional elliptic equation with concave-convex nonlinearities: {(-Delta)(alpha)u + V-lambda(x)u = a(x)vertical bar u vertical bar(q-2)u + b(x)vertical bar u vertical bar(p-2)u in R-N, u >= 0 in R-N, where 0 < alpha < 1, N > 2 alpha, 1 < q < 2 < p < 2(alpha)*; with 2(alpha)*= 2N/(N - 2 alpha), the potential V-lambda(x) = lambda V+(x)- V-(x) with V-+/- = max{+/- V, 0} and the parameter lambda > 0. Our multiplicity results are based on studying the decomposition of the Nehari manifold.