Generalized n-Laplacian: semilinear Neumann problem with the critical growth

Abstract

Applying the generalized Moser-Trudinger inequality without boundary condition, the Mountain Pass Theorem and the Ekeland Variational Principle we prove the existence and multiplicity of nontrivial weak solutions to a semilinear Neumann problem concerning a generalized n-Laplace equation with the nonlinearity having the critical growth.

Keywords

• Orlicz-Sobolev spaces
• Mountain Pass Theorem
• Palais-Smale sequence
• Ekeland Variational Principle