Existence of Solutions for a Perturbed N-Laplacian Boundary Value Problem with Critical Growth

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 Z(2)-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.