In this paper, we consider the following 1-Laplacian problem
where , is a periodic potential and 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.
Accepted:
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Shi-Ying Wang 1; Peng Chen 1; Lin Li 2
@article{CRMATH_2022__360_G4_297_0, author = {Shi-Ying Wang and Peng Chen and Lin Li}, title = {Ground state solution for a non-autonomous {1-Laplacian} problem involving periodic potential in $\protect \mathbb{R}^N$}, journal = {Comptes Rendus. Math\'ematique}, pages = {297--304}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.276}, language = {en}, }
TY - JOUR AU - Shi-Ying Wang AU - Peng Chen AU - Lin Li TI - Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in $\protect \mathbb{R}^N$ JO - Comptes Rendus. Mathématique PY - 2022 SP - 297 EP - 304 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.276 LA - en ID - CRMATH_2022__360_G4_297_0 ER -
%0 Journal Article %A Shi-Ying Wang %A Peng Chen %A Lin Li %T Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in $\protect \mathbb{R}^N$ %J Comptes Rendus. Mathématique %D 2022 %P 297-304 %V 360 %I Académie des sciences, Paris %R 10.5802/crmath.276 %G en %F CRMATH_2022__360_G4_297_0
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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