RESEARCH ARTICLE
Ground state solutions for Schrödinger–Poisson systems on with a weighted critical exponent
Yao Du,
Jiabao Su,
Yao Du
School of Mathematical Sciences, Capital Normal University, Beijing, People's Republic of China
Search for more papers by this authorCorresponding Author
Jiabao Su
School of Mathematical Sciences, Capital Normal University, Beijing, People's Republic of China
Correspondence
Jiabao Su, School of Mathematical Sciences, Capital Normal University, Beijing 100048, People's Republic of China.
Email: [email protected]
Communicated by: C. Ji
Search for more papers by this authorYao Du,
Jiabao Su,
Yao Du
School of Mathematical Sciences, Capital Normal University, Beijing, People's Republic of China
Search for more papers by this authorCorresponding Author
Jiabao Su
School of Mathematical Sciences, Capital Normal University, Beijing, People's Republic of China
Correspondence
Jiabao Su, School of Mathematical Sciences, Capital Normal University, Beijing 100048, People's Republic of China.
Email: [email protected]
Communicated by: C. Ji
Search for more papers by this authorFirst published: 29 December 2022
Funding information: Supported by NSFC (12271373, 12171326) and KZ202010028048.
Abstract
In this paper, we are interested in the existence of ground state solutions for the weighted critical Schrödinger–Poisson systems. The weighted critical exponent may be the Hénon–Sobolev, the Sobolev or the Hardy–Sobolev critical exponent. Moreover, the potentials are power type, which may be singular at origin or unbounded. Due to the presence of Possion term, we can not directly obtain the boundedness of the Palais–Smale sequences of the associated functional for some cases. The Pohozaev identity, the minimax principle and some techniques are used to overcome the difficulties.
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