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

We deal with the existence and concentration of positive solutions for the following p-fractional Schrödinger equation: εsp(-Δ)psu+V(x)|u|p-2u=f(u)+γ|u|ps∗-2uinRN,where ε> 0 is a small parameter, s∈ (0 , 1) , p∈ (1 , ∞) , N> sp, γ∈ { 0 , 1 } , ps∗=NpN-sp is the fractional critical Sobolev exponent, (-Δ)ps 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.