Geodesic
Indefinite Planar Problem with Exponential Critical Growth
Journal of convex analysis, Tome 29 (2022) no. 2, pp. 361-37
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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.
Classification : 35J60, 35B33
Mots-clés : Exponential critical growth, Trudinger–Moser inequality, variational methods, indefinite problems 
@article{JCA_2022_29_2_JCA_2022_29_2_a3,
     author = {M. F. Furtado and K. C. V. Sousa},
     title = {Indefinite {Planar} {Problem} with {Exponential} {Critical} {Growth}},
     journal = {Journal of convex analysis},
     pages = {361--37},
     year = {2022},
     volume = {29},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_2_JCA_2022_29_2_a3/}
}
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M. F. Furtado; K. C. V. Sousa. Indefinite Planar Problem with Exponential Critical Growth. Journal of convex analysis, Tome 29 (2022) no. 2, pp. 361-37. http://geodesic.mathdoc.fr/item/JCA_2022_29_2_JCA_2022_29_2_a3/