The multiplicity of solutions for the critical Schrödinger–Poisson system with competing potentials

This paper deals with the Kirchhoff-Schrödinger-Poisson system involving sign-changing weight functions. We prove the existence and multiplicity of solutions to the system. Our main results are based on the method of Nehari manifold.

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Existence and multiplicity of solutions for Kirchhoff–Schrödinger–Poisson system with critical growth

International Journal of Mathematics ◽

10.1142/s0129167x22500082 ◽

2021 ◽

Author(s):

Guofeng Che ◽

Haibo Chen

Keyword(s):

Variational Methods ◽

Critical Growth ◽

Poisson System ◽

Nontrivial Solutions ◽

Multiplicity Of Solutions ◽

Existence And Multiplicity

This paper is concerned with the following Kirchhoff–Schrödinger–Poisson system: [Formula: see text] where constants [Formula: see text], [Formula: see text] and [Formula: see text] are the parameters. Under some appropriate assumptions on [Formula: see text], [Formula: see text] and [Formula: see text], we prove the existence and multiplicity of nontrivial solutions for the above system via variational methods. Some recent results from the literature are greatly improved and extended.

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Multiplicity of solutions for Schrödinger-Poisson system with critical exponent in $\mathbb{R}^{3}$

AIMS Mathematics ◽

10.3934/math.2021126 ◽

2021 ◽

Vol 6 (3) ◽

pp. 2059-2077

Author(s):

Xueqin Peng ◽

◽

Gao Jia ◽

Chen Huang ◽

Keyword(s):

Critical Exponent ◽

Poisson System ◽

Multiplicity Of Solutions

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Existence and multiplicity of solutions of Schrödinger—Poisson systems with radial potentials

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210512001382 ◽

2014 ◽

Vol 144 (2) ◽

pp. 319-332 ◽

Cited By ~ 2

Author(s):

Anran Li ◽

Jiabao Su ◽

Leiga Zhao

Keyword(s):

Variational Methods ◽

Infinitely Many Solutions ◽

Poisson System ◽

Radial Solutions ◽

Radial Functions ◽

Multiplicity Of Solutions ◽

Nonlinear Schrödinger ◽

Existence And Multiplicity ◽

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In this paper, we deal with the nonlinear Schrödinger–Poisson systemwhere λ > 0, V and Q are radial functions, which can be vanishing or coercive at ∞. With assumptions on f just in a neighbourhood of the origin, existence and multiplicity of non-trivial radial solutions are obtained via variational methods. In particular, if f is sublinear and odd near the origin, we obtain infinitely many solutions of (SP)λ for any λ < 0.

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