Abstract
In this paper, we establish a weighted Trudinger–Moser type inequality and as the application of this result by using the Galerkin methods and a linking theorem, we prove the existence of weak solutions for the following class of elliptic systems: when the potential V is neither bounded away from zero, nor bounded from above. The nonlinear terms and are superlinear at infinity and have subcritical or critical exponential growth.
2010 AMS Subject Classifications:
Disclosure statement
No potential conflict of interest was reported by the author(s).