Ground state sign-changing solutions for fractional Laplacian equations with critical nonlinearity

Abstract

In this paper, we investigate the existence of the least energy sign-changing solutions for nonlinear elliptic equations driven by nonlocal integro-differential operators with critical nonlinearity. By using constrained minimization method and topological degree theory, we obtain a least energy sign-changing solution for them under much weaker conditions. As a particular case, we drive an existence theorem of sign-changing solutions for the fractional Laplacian equations with critical growth.

Keywords

• fractional laplacian equation
• sign-changing solution
• ekeland's variational principle
• brouwer's degree theory
• variational methods