Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials

Abstract

This paper is concerned with the following fractional Schrödinger equations involving critical exponents: (−Δ)αu+V(x)u=k(x)f(u)+λ|u|2α∗−2uinRN, where (−Δ)α is the fractional Laplacian operator with α∈(0,1), N≥2, λ is a positive real parameter and 2α∗=2N/(N−2α) is the critical Sobolev exponent, V(x) and k(x) are positive and bounded functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space and the minimax arguments, we obtain the existence of a nontrivial radially symmetric weak solution for the above-mentioned equations without assuming the Ambrosetti–Rabinowitz condition on the subcritical nonlinearity.