On some quasilinear problem of nonvariational structure and involving exponential critical growth conditions

Abstract

In this paper, we establish the existence of at least one nontrivial solution for a nonhomogeneous problem having a nonvariational structure. The nonlinearity term enjoys a critical exponential growth. Our main tools are Galerkin approximative method and the degree theory of some special type of mappings.

Keywords:

• N-Laplacian
• Trudinger-Moser inequality
• critical exponential growth
• degree theory
• Galerkin method

AMS Subject Classifications:

• 35D30
• 35J20
• 35J61
• 58E05