Nonlinear Elliptic Equations with Maximal Growth Range - Santaria Leuyacc, Yony Raúl (2017)
In this work we are interested in studying the existence of nontrivial weak solutions for a class of nonlinear elliptic equations defined in a bounded domain in dimension two, where the nonlinearities possess maximal exponential growth range motivated by Trudinger-Moser inequalities in Lorentz-Sobolev spaces. In order to study the solvability we use a variational approach. More specifically, we use mountain pass theorem combined with Trudinger-Moser type inequalities.