SIGN-CHANGING SOLUTIONS FOR NON-LOCAL ELLIPTIC EQUATIONS

This article concerns the existence of sign-changing solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions, -L(K)u = f(x, u), x is an element of Omega, u = 0, x is an element of R-n \ Omega, where Omega subset of R-n (n >= 2) is a bounded, smooth domain and the nonlinear term f satisfies suitable growth assumptions. By using Brouwer's degree theory and Deformation Lemma and arguing as in [2], we prove that there exists a least energy sign-changing solution. Our results generalize and improve some results obtained in [27].