Ground State Solution for the Logarithmic Schrödinger–Poisson System with Critical Growth

In this paper we investigate a class of logarithmic Schrödinger–Poisson system with critical growth which are from physically relevant backgrounds. Under suitable assumptions on the potential V ( x ), we obtain the existence of ground state solution for ε > 0 sufficiently small via using a constr...

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Veröffentlicht in:Qualitative theory of dynamical systems 2025-02, Vol.24 (1), Article 16
Hauptverfasser: Cai, Yaqing, Zhao, Yulin
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper we investigate a class of logarithmic Schrödinger–Poisson system with critical growth which are from physically relevant backgrounds. Under suitable assumptions on the potential V ( x ), we obtain the existence of ground state solution for ε > 0 sufficiently small via using a constrained minimization on a Nehari manifold and some new techniques. Specially, by restricting the least energy c to a suitable interval, we overcome some difficulties brought by the critical term u 5 for restoring the compactness of the minimizing sequence of the least energy c .
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01174-x