Existence and concentration of positive solutions for p-fractional Schrodinger equations

We deal with the existence and concentration of positive solutions for the following p-fractional Schrodinger equation: epsilon(sp) (-Delta)(p)(s)u + V(x)vertical bar u vertical bar(p-2)u = f (u) + gamma vertical bar u vertical bar(ps* -2)u in R-N , where epsilon > 0 is a small parameter, s is an element of (0, 1), p is an element of (1, infinity), N > sp, gamma is an element of{0, 1}, p(s)* = Np/N-sp is the fractional critical Sobolev exponent, (-Delta)(p)(s) is the fractional p-Laplacian operator, V is a continuous positive potential having a local minimum and f is a superlinear continuous function with subcritical growth. The main results are obtained by using penalization techniques and suitable variational arguments.