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Existence of solutions to Schrödinger‐Poisson systems with critical and supercritical nonlinear terms
Author(s) -
Li Yuhua,
Gu Hua
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5507
Subject(s) - supercritical fluid , mathematics , nonlinear system , compact space , schrödinger's cat , poisson distribution , class (philosophy) , function (biology) , variational method , mathematical analysis , physics , thermodynamics , quantum mechanics , statistics , artificial intelligence , evolutionary biology , biology , computer science
In this paper, the existence of nontrivial solutions to a class of Schrödinger‐Poisson systems with critical and supercritical nonlinear terms is obtained via variational methods. By using the potential function, a compactness imbedding result is obtained. The properties of potential function play an important role for insuring variational setting.