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Comptes Rendus. Mathématique
Partial differential equations
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.

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: https://doi.org/10.5802/crmath.175
Classification: 35J20,  35A23,  35Q55,  35J61
Keywords: 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
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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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