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Existence of ground state solution for Schrödinger-Poisson systems with critical term. (English) Zbl 1463.35055

Summary: The existence of a positive ground state solution for a class of Schrödinger-Poisson systems with nonlinear critical growth and nonlocal critical growth was studied by using the Nehari manifold method. Firstly, the Nehari manifold corresponding to the system was proved to be nonempty by algebraic method. Then, the range of the lowest energy level value on the Nehari manifold was estimated. Finally, the existence of the positive ground state solution of the system was obtained by means of concentration-compactness principle.

MSC:

35B09 Positive solutions to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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