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

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...

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Bibliographic Details
Published in:Mathematische Nachrichten 2024-03, Vol.297 (3), p.861-877
Main Authors: Alves, Claudianor Oliveira, de Holanda, Angelo Roncalli Furtado
Format: Article
Language:English
Subjects:
critical growth
degenerate elliptic equations
Elliptic functions
Sobolev space
Trudinger–Moser inequality
variational methods
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Summary: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202300171