Journal of Convex Analysis 29 (2022), No. 2, 361--370
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
[Abstract-pdf]
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 sign-changing 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.
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