Existence of the solution for a class of the semilinear degenerate elliptic equation involving the Grushin operator in R2$\mathbb {R}^2$: The interaction between Grushin's critical exponent and exponential growth

Claudianor Oliveira Alves and Angelo Roncalli Furtado de Holanda

Mathematische Nachrichten, 2024, vol. 297, issue 3, 861-877

Abstract: In this work, we study the existence of the solution for a class of semilinear degenerate elliptic equations in the whole space R2$\mathbb {R}^{2}$ involving the Grushin operator and a nonlinearity that involves the Grushin's critical growth and the exponential growth. The existence of at least one nontrivial weak solution is done by combining the mountain‐pass theorem, Trudinger–Moser inequality, and a version of a result due to Lions for the exponential growth in R2$\mathbb {R}^{2}$ in the corresponding weighted Sobolev space.

Date: 2024
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https://doi.org/10.1002/mana.202300171

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:3:p:861-877

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