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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Accepted:

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Keywords: Schrödinger–Poisson–Slater type equation, ground state, Coulomb–Sobolev inequality

Chunyu Lei ^{1};
Yutian Lei ^{2}

@article{CRMATH_2021__359_2_219_0, 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}, }

TY - JOUR AU - Chunyu Lei AU - Yutian Lei TI - On the existence of ground states of an equation of Schrödinger–Poisson–Slater type JO - Comptes Rendus. Mathématique PY - 2021 SP - 219 EP - 227 VL - 359 IS - 2 PB - Académie des sciences, Paris DO - 10.5802/crmath.175 LA - en ID - CRMATH_2021__359_2_219_0 ER -

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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