Existence of nontrivial solutions for fractional Schrödinger equations with critical or supercritical growth

In this paper, we study the following fractional Schrödinger equation with critical or supercritical growth urn:x-wiley:mma:media:mma5441:mma5441-math-0001 where 0 < s < 1, N > 2 s , λ > 0, , , ( − Δ) s denotes the fractional Laplacian of order s and f is a continuous superlinear but subcritical function. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 by variational methods. Our main contribution is related to the fact that we are able to deal with the case .