Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth

Abstract

In this paper, we investigate a perturbed elliptic boundary value problem that exhibits critical growth characterized by a Trudinger–Moser-type inequality. Our primary focus is to establish the existence of two nontrivial solutions. This is achieved by employing a combination of the Trudinger–Moser-type inequality and a linking theorem based on the Z2-cohomological index. The main feature and novelty of this paper lies in extending the equation to N-Laplacian boundary value problems utilizing the aforementioned methods. This extension not only broadens the applicability of these techniques but also enriches the research outcomes in the field of nonlinear analysis.

Keywords

• <i>N</i>-Laplacian
• critical growth
• linking theorem
• perturbation
• ℤ₂-cohomological index