Generalized Moser-Trudinger inequality for unbounded domains and its application

Abstract

We give a version of the Moser-Trudinger inequality for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces on unbounded domains in. Applying this result and the Mountain Pass Theorem we study the existence of non-trivial weak solutions to the generalized n-Laplace equation.

Keywords

• Orlicz-Sobolev spaces
• Mountain pass theorem
• Palais-Smale sequence