Elliptic problem involving logarithmic weight under exponential nonlinearities growth

Abstract

AbstractIn this paper, we study the nonlinear weighted elliptic problem where B is the unit ball of , , and the singular logarithm weight with the limiting exponent in the Trudinger–Moser embedding. The nonlinearities are critical or subcritical growth in view of Trudinger–Moser inequalities. We prove the existence of nontrivial solutions via the critical point theory. In the critical case, the associated energy functional does not satisfy the compactness condition. We give a new growth condition and we point out its importance for checking the Palais–Smale compactness condition.