The least energy sign-changing solution for a nonlocal problem

Abstract

In this paper, we consider the following general nonlocal problem: −LKu=f(x,u) in Ω and u = 0 in ℝN∖Ω, where Ω⊂ℝN is a bounded domain with Lipschitz boundary ∂Ω and LK is an integrodifferential operator of fractional Laplacian type. Combining constraint variational method and quantitative deformation lemma, we verify that the problem possesses one least energy sign-changing solution u0. Moreover, the energy of u0 is strictly larger than the ground state energy.