Existence of infinitely many solutions for elliptic boundary-value problems with nonsymmetrical critical nonlinearity

Abstract

In this paper, we study a semilinear elliptic boundary-value problem involving nonsymmetrical term with critical growth on a bounded smooth domain in $mathbb{R}^n$. We show the existence of infinitely many weak solutions under the presence of some symmetric sublinear term, the corresponding critical values of the variational functional are negative and go to zero.

Keywords

• Dirichlet problem
• critical growth
• non-symmetric perturbation
• infinitely many solutions.