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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Mots clés : Schrödinger–Poisson–Slater type equation, ground state, Coulomb–Sobolev inequality
@article{CRMATH_2021__359_2_219_0,
author = {Lei, Chunyu and Lei, Yutian},
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},
url = {http://www.numdam.org/articles/10.5802/crmath.175/}
}
TY - JOUR AU - Lei, Chunyu AU - Lei, Yutian 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 UR - http://www.numdam.org/articles/10.5802/crmath.175/ DO - 10.5802/crmath.175 LA - en ID - CRMATH_2021__359_2_219_0 ER -
%0 Journal Article %A Lei, Chunyu %A Lei, Yutian %T On the existence of ground states of an equation of Schrödinger–Poisson–Slater type %J Comptes Rendus. Mathématique %D 2021 %P 219-227 %V 359 %N 2 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.175/ %R 10.5802/crmath.175 %G en %F CRMATH_2021__359_2_219_0
Lei, Chunyu; Lei, Yutian. On the existence of ground states of an equation of Schrödinger–Poisson–Slater type. Comptes Rendus. Mathématique, Tome 359 (2021) no. 2, pp. 219-227. doi : 10.5802/crmath.175. http://www.numdam.org/articles/10.5802/crmath.175/
[1] Multiple bounded states for Schrödinger–Poisson problem, Commun. Contemp. Math., Volume 10 (2008) no. 3, pp. 391-404 | DOI | Zbl
[2] Maximizers for Gagliardo–Nirenberg inequalities and related non-local problems, Math. Ann., Volume 360 (2014) no. 3-4, pp. 653-673 | DOI | MR | Zbl
[3] Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces, Trans. Am. Math. Soc., Volume 370 (2018) no. 11, pp. 8285-8310 | DOI | MR | Zbl
[4] On bound states concentrating on spheres for the Maxwell–Schrödinger equation, SIAM J. Math. Anal., Volume 37 (2005) no. 1, pp. 321-342 | DOI | Zbl
[5] On the radiality of constrained minimizers to the Schrödinger–Poisson–Slater energy, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 29 (2012) no. 3, pp. 369-376 | DOI | Numdam | Zbl
[6] Ground and bound states for a static Schrödinger–Poisson–Slater problem, Commun. Contemp. Math., Volume 14 (2012) no. 1, 1250003, 22 pages | Zbl
[7] Qualitative analysis for the static Hartree-type equations, SIAM J. Math. Anal., Volume 45 (2013) no. 1, pp. 388-406 | MR | Zbl
[8] Existence and nonexistence of positive solutions for a static Schrödinger–Poisson–Slater equation, J. Differ. Equations, Volume 266 (2019) no. 9, pp. 5912-5941 | Zbl
[9] The Schrödinger–Poisson equation under the effect of a nonlinear local term, J. Funct. Anal., Volume 237 (2006) no. 2, pp. 655-674 | DOI | MR | Zbl
[10] On the Schrödinger–Poisson–Slater system: behavior of minimizers, radial and nonradial cases, Arch. Ration. Mech. Anal., Volume 198 (2010) no. 1, pp. 349-368 | DOI | MR | Zbl
[11] Cluster solutions for the Schrödinger–Poisson–Slater problem around a local minimun of potential, Rev. Mat. Iberoam., Volume 27 (2011) no. 1, pp. 253-271 | DOI | Zbl
[12] Ground state solutions of Nehari–Pohozaev type for Schrödinger–Poisson problems with general potentials, Discrete Contin. Dyn. Syst., Volume 37 (2017) no. 9, pp. 4973-5002 | DOI | Zbl
[13] Minimax theorems, Progress in Nonlinear Differential Equations and their Applications, 24, Birkhäuser, 1996 | MR | Zbl
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