Existence of multiple solutions to elliptic problems of Kirchhoff type with critical exponential growth

Abstract

In this article, we study elliptic problems of Kirchhoff type in dimension $ N \geq 2$, whose nonlinear term has a critical exponential growth. Using variational tools, we establish the existence of at least two nontrivial and nonnegative solutions.

Keywords

• Trudinger-Moser inequality
• exponential growth
• Kirchhoff equation
• critical point
• energy functional
• Ekeland's lemma
• Mountain Pass Theorem