MULTI-BUMP SOLUTIONS FOR FRACTIONAL SCHRODINGER EQUATION WITH ELECTROMAGNETIC FIELDS AND CRITICAL NONLINEARITY

In this article, we consider the existence of multi-bump solutions for a class of the fractional Schrodinger equation with external magnetic field and critical nonlinearity in R-N: (-Delta)(A)(s)u + (lambda V(x) + Z(x))u = beta f(vertical bar u vertical bar(2))u + vertical bar u vertical bar(2s)*(-2) u, where f is a continuous function satisfying Ambrosetti-Rabinowitz con- dition, and V : R-N -> R has a potential well Omega := intV(-1) (0) which possesses k disjoint bounded components Omega := boolean OR(k)(j=1)Omega(j). By using variational methods, we prove that if the parameter lambda > 0 is large enough, then the equation has at least 2(k) - 1 multi-bump solutions.