Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in $\protect \mathbb{R}^N$

Wang, Shi-Ying; Chen, Peng; Li, Lin

doi:10.5802/crmath.276

Équations aux dérivées partielles

Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in

ℝ^{N}

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

Comptes Rendus. Mathématique, Tome 360 (2022) no. G4, pp. 297-304.

Résumé

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

- Δ_{1} u + V (x) \frac{u}{| u |} = f (x, u), x \in ℝ^{N}, u > 0, u \in B V (ℝ^{N}),

where $Δ_{1} u = div (\frac{D u}{| D u |})$ , $V$ 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.

Reçu le : 2021-09-07
Accepté le : 2021-09-26
Accepté après révision le : 2021-10-15
Publié le : 2022-04-26

DOI : 10.5802/crmath.276

Classification : 35J62, 35J75

Affiliations des auteurs :

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

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     title = {Ground state solution for a non-autonomous {1-Laplacian} problem involving periodic potential in $\protect \mathbb{R}^N$},
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Wang, Shi-Ying; Chen, Peng; Li, Lin. Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in $\protect \mathbb{R}^N$. Comptes Rendus. Mathématique, Tome 360 (2022) no. G4, pp. 297-304. doi : 10.5802/crmath.276. http://www.numdam.org/articles/10.5802/crmath.276/

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