Multiplicity of solutions for quasilinear elliptic problems involving $\Phi$-Laplacian operator and critical growth

Abstract

In this paper, we study a class of quasilinear elliptic equations with $\Phi$-Laplacian operator and critical growth. Using the symmetric mountain pass theorem and the concentration-compactness principle, we demonstrate that there exists $\lambda_i>0$ such that our problem admits $i$ pairs of nontrivial weak solutions provided $\lambda\in (0, \lambda_i)$.

Keywords

• quasilinear elliptic equation
• critical exponent
• variational method