Multiple sign-changing solutions for fractional Schrödinger equations involving critical or supercritical exponent

Abstract

In this article, we focus on the following fractional Schrödinger equation involving critical or supercritical exponent (P)(−Δ)su+λV(x)u=|u|p−2u+Q(x)|u|q−2u,x∈RN,where 0<s<1, (−Δ)s denotes the fractional Laplacian of order s, λ≥1, N>2s, 2<p<2s∗≤q and 2s∗=2NN−2s. Under suitable assumptions on V(x) and Q(x), we prove that the above equation possesses k pairs of sign-changing solutions for large λ by using of truncation technique.