Multiplicity results for elliptic problems with critical exponential growth

Abstract

We prove new multiplicity results for some elliptic problems with critical exponential growth. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter $μ> 0$. In particular, the number of solutions goes to infinity as $μ\to \infty$. The proof is based on an abstract critical point theorem.

Theorems & Definitions (10)

• Theorem 1.1
• Corollary 1.2
• Theorem 1.3
• Theorem 1.4
• Theorem 1.5
• Theorem 1.6
• Theorem 1.7
• Theorem 2.1: Pe23
• proof : Proof of Theorem \ref{['Theorem 2']}
• proof : Proof of Theorem \ref{['Theorem 4']}