Existence and number of solutions for a class of semilinear Schrodinger equations

Using an argument of concentration-compactness type we study the problem -Delta u + lambda V(x)u = vertical bar u vertical bar(p-2) u, x is an element of R-N, where 2 < p < 2* and the set {x is an element of R-N : V(x) < b} is nonempty and. has finite measure for some b > 0. In particular, we show that if V-1(0) has nonempty interior, then the number of solutions increases with A. We also study concentration of solutions on the set V-1(0) as lambda -> infinity.