
Journal of Convex Analysis 29 (2022), No. 2, 361370 Copyright Heldermann Verlag 2022 Indefinite Planar Problem with Exponential Critical Growth Marcelo F. Furtado Dept. of Mathematics, University of Brasilia, Brasilia, Brazil mfurtado@unb.br Karla C. V. Sousa Dept. of Mathematics, University of Brasilia, Brasilia, Brazil karlakcvs@gmail.com [Abstractpdf] We obtain existence of solution for the equation $$ \Delta u + \frac{1}{2}(x \cdot \nabla u) = a(x)f(u),\quad x\in\mathbb{R}^2, $$ where $a$ is a continuous signchanging potential and the superlinear function $f$ has an exponential critical growth. Keywords: Exponential critical growth, Trudinger–Moser inequality, variational methods, indefinite problems. MSC: 35J60; 35B33. [ Fulltextpdf (114 KB)] for subscribers only. 