On the existence of ground states of an equation of Schrödinger–Poisson–Slater type

Chunyu Lei; Yutian Lei

doi:10.5802/crmath.175

Équations aux dérivées partielles

On the existence of ground states of an equation of Schrödinger–Poisson–Slater type

Chunyu Lei ¹ ; Yutian Lei ²

¹ Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
² Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 219-227.

Résumé

We study the existence of ground states of a Schrödinger–Poisson–Slater type equation with pure power nonlinearity. By carrying out the constrained minimization on a special manifold, which is a combination of the Pohozaev manifold and Nehari manifold, we obtain the existence of ground state solutions of this system.

Reçu le : 2020-12-11
Révisé le : 2020-12-29
Accepté le : 2020-12-29
Publié le : 2021-03-17

DOI : 10.5802/crmath.175

Classification : 35J20, 35A23, 35Q55, 35J61
Mots clés : Schrödinger–Poisson–Slater type equation, ground state, Coulomb–Sobolev inequality

Affiliations des auteurs :

Chunyu Lei ¹ ; Yutian Lei ²

¹ Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
² Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Chunyu Lei and Yutian Lei},
     title = {On the existence of ground states of an equation of {Schr\"odinger{\textendash}Poisson{\textendash}Slater} type},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {219--227},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {2},
     year = {2021},
     doi = {10.5802/crmath.175},
     language = {en},
}

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Chunyu Lei; Yutian Lei. On the existence of ground states of an equation of Schrödinger–Poisson–Slater type. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 219-227. doi : 10.5802/crmath.175. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.175/

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