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Ground state solutions for fractional Choquard equations involving upper critical exponent
Nonlinear Analysis, 2020In this article, we study the following fractional Choquard equation involving upper critical exponent ( − Δ ) s u + V ( x ) u = λ f ( x , u ) + [ | x | − μ ∗ | u | 2 μ , s ∗ ] | u | 2 μ , s ∗ − 2 u , x ∈ R N , where λ > 0 , 0 s 1 , ( − Δ ) s denotes the
Quanqing Li, K. Teng, Jian Zhang
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UNIQUENESS OF GROUND STATE SOLUTIONS
Acta Mathematica Scientia, 1988Summary: We discuss the uniqueness of ground state solutions of the problem \[ \Delta u+f(u)=0\quad in\quad R^ n;\quad u(x)\to 0\quad as\quad | x| \to \infty, \] where \(N>2\), f(u) satisfies some conditions which ensure the existence of a ground state solution.
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Ground-state solutions of the Hubbard model
Physical Review B, 1983The ground-state solutions of the Hubbard model are studied. A two-sublattice formalism is developed in order to allow ferromagnetic, ferrimagnetic, and antiferromagnetic solutions. The electronic structure is solved within the Bethe-lattice method and the size of the local moments on each sublattice are determinated in a self-consistent manner.
J. Dorantes-Dávila +2 more
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Communications in Contemporary Mathematics, 2019
We are concerned with the existence and concentration behavior of ground state solutions of the fractional Schrödinger–Poisson system with critical nonlinearity [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text ...
Zhipeng Yang, Yuanyang Yu, Fukun Zhao
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We are concerned with the existence and concentration behavior of ground state solutions of the fractional Schrödinger–Poisson system with critical nonlinearity [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text ...
Zhipeng Yang, Yuanyang Yu, Fukun Zhao
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Ground state solution for strongly indefinite Choquard system
Nonlinear Analysis, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Jianqing, Zhang, Qian
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Milan Journal of Mathematics, 2019
In this paper, we study the following class of nonlinear equations: $$ -\Delta u+V(x) u = \left[|x|^{-\mu}*(Q(x)F(u))\right]Q(x)f(u),\quad x\in\mathbb{R}^2, $$ where $V$ and $Q$ are continuous potentials, which can be unbounded or vanishing at infintiy, $
F. Albuquerque +2 more
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In this paper, we study the following class of nonlinear equations: $$ -\Delta u+V(x) u = \left[|x|^{-\mu}*(Q(x)F(u))\right]Q(x)f(u),\quad x\in\mathbb{R}^2, $$ where $V$ and $Q$ are continuous potentials, which can be unbounded or vanishing at infintiy, $
F. Albuquerque +2 more
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Ground state solutions for quasilinear scalar field equations arising in nonlinear optics
Nonlinear Differential Equations and Applications NoDEA, 2020In this paper, we study a class of quasilinear elliptic equations which appears in nonlinear optics. By using the mountain pass theorem together with a technique of adding one dimension of space (Hirata et al.
A. Pomponio, Tatsuya Watanabe
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Ground state solutions for a coupled Kirchhoff‐type system
Mathematical Methods in the Applied Sciences, 2015In this paper, we consider the coupled Kirchhoff‐type system urn:x-wiley:mma:media:mma3414:mma3414-math-0488 where ε is a small positive parameter and ai>0, bi≥0 are constants for i = 1,2, P,Q are positive continuous potentials satisfying some conditions.
Lü, Dengfeng, Xiao, Jianhai
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Mathematische Nachrichten, 2019
In this paper, we study the following critical fractional Schrödinger–Poisson system ε2s(−Δ)su+V(x)u+ϕu=P(x)f(u)+Q(x)|u|2s∗−2u,inR3,ε2t(−Δ)tϕ=u2,inR3,where ε>0 is a small parameter, s∈(34,1),t∈(0,1) and 2s+2t>3 , 2s∗:=63−2s is the fractional critical ...
Zhipeng Yang, Yuanyang Yu, Fukun Zhao
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In this paper, we study the following critical fractional Schrödinger–Poisson system ε2s(−Δ)su+V(x)u+ϕu=P(x)f(u)+Q(x)|u|2s∗−2u,inR3,ε2t(−Δ)tϕ=u2,inR3,where ε>0 is a small parameter, s∈(34,1),t∈(0,1) and 2s+2t>3 , 2s∗:=63−2s is the fractional critical ...
Zhipeng Yang, Yuanyang Yu, Fukun Zhao
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The Ground State Solutions to Discrete Nonlinear Choquard Equations with Hardy Weights
Bulletin of the Iranian Mathematical Society, 2023Lidan Wang
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