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Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in N
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 297-304.

In this paper, we consider the following 1-Laplacian problem

-Δ 1 u+V(x)u |u|=f(x,u),x N ,u>0,uBV N ,

where Δ 1 u=div(Du |Du|), V is a periodic potential and f is periodic and verifies the super-primary condition at infinity. By the Nehari type manifold method, the concentration compactness principle and some analysis techniques, we show the 1-Laplacian equation has a ground state solution.

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DOI : 10.5802/crmath.276
Classification : 35J62, 35J75

Shi-Ying Wang 1 ; Peng Chen 1 ; Lin Li 2

1 School of Science, China Three Gorges University, Hubei 443002, China
2 School of Mathematics and Statistics & Chongqing Key Laboratory of Economic and Social Application Statistics, Chongqing Technology and Business University, Chongqing 400067, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Ground state solution for a non-autonomous {1-Laplacian} problem involving periodic potential in $\protect \mathbb{R}^N$},
     journal = {Comptes Rendus. Math\'ematique},
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     publisher = {Acad\'emie des sciences, Paris},
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Shi-Ying Wang; Peng Chen; Lin Li. Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in $\protect \mathbb{R}^N$. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 297-304. doi : 10.5802/crmath.276. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.276/

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