Sign-changing solutions for non-local elliptic equations

Abstract

This article concerns the existence of sign-changing solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions, $$\displaylines{ -\mathcal{L}_Ku=f(x,u),\quad x\in \Omega, \cr u=0,\quad x\in \mathbb{R}^n\setminus\Omega, }$$ where $\Omega\subset\mathbb{R}^n\; (n\geq2)$ 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]

Keywords

• Brouwer's degree theory
• sign-changing solutions
• non-local elliptic equations
• deformation Lemma