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On the existence of ground states of an equation of Schrödinger–Poisson–Slater type
Chunyu Lei1 ; Yutian Lei2
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.

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.

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DOI : 10.5802/crmath.175
Classification : 35J20, 35A23, 35Q55, 35J61
Mots clés : Schrödinger–Poisson–Slater type equation, ground state, Coulomb–Sobolev inequality
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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     journal = {Comptes Rendus. Math\'ematique},
     pages = {219--227},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {2},
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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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