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• W3113175092 abstract "In this paper, a class of Schrodinger-Poisson system involving multiple competing potentials and critical Sobolev exponent is considered. Such a problem cannot be studied with the same argument of the nonlinear term with only a positive potential, because the weight potentials set ${Q_i(x)|1le i le m}$ contains nonpositive, sign-changing, and nonnegative elements. By introducing the ground energy function and subtle analysis, we first prove the existence of ground state solution $v_varepsilon$ in the semiclassical limit via the Nehari manifold and concentration-compactness principle. Then we show that $v_varepsilon$ converges to the ground state solution of the associated limiting problem and concentrates at a concrete set characterized by the potentials. At the same time, some properties for the ground state solution are also studied. Moreover, a sufficient condition for the nonexistence of the ground state solution is obtained." @default.
• W3113175092 created "2020-12-21" @default.
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• W3113175092 date "2020-12-16" @default.
• W3113175092 modified "2023-09-23" @default.
• W3113175092 title "Semiclassical solutions for critical Schrodinger-Poisson systems involving multiple competing potentials" @default.
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• W3113175092 hasPublicationYear "2020" @default.
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