Sign-changing solutions for non-local elliptic equations with asymptotically linear term

Abstract

In this article, we study the existence of sign-changing solutions for a problem driven by a non-local integrodifierential operator with homogeneous Dirichlet boundary condition {-LKu = f(x u) in u = 0 in Rn/Ω (1) where Ω ⊂Rn(n ≥ 2) is a bounded, smooth domain and f(x u) is asymptotically linear at infinity with respect to u. By introducing some new ideas and combining constraint variational method with the quantitative deformation lemma, we prove that there exists a sign-changing solution of problem (1).