Multiplicity result for some degenerate elliptic problem involving critical exponential growth in $ \mathbb{R}^N$

Abstract

In this paper, we study some nonhomogeneous degenerate elliptic equation in dimension $ N,$ $ N \geq 3 $ with nonlinearity term having an exponential growth and does not satisfy the Ambrosetti-Rabinowitz (AR) condition. Using a variational tools, we establish the existence of at least two positive solutions.