Schrödinger‐Poisson system with Hardy‐Littlewood‐Sobolev critical exponent
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DOI: 10.1002/mma.5694
Abstract: In this paper, we consider the following Schrödinger‐Poisson system: −Δu+λϕ|u|2α∗−2u=∫R3|u|2β∗|x−y|3−βdy|u|2β∗−2u,inR3,(−Δ)α2ϕ=Aα−1|u|2α∗,inR3, where parameters α,β∈(0,3),λ>0, Aα=Γ(3−α2)2απ32Γ(α2) , 2α∗=3+α , and 2β∗=3+β are the Hardy‐Littlewood‐Sobolev critical exponents. For α0, we prove the existence of nonnegative groundstate solution to… read more here.
Keywords: dinger poisson; system; hardy littlewood; littlewood sobolev ... See more keywords
Nontrivial solutions for the fractional Schrödinger‐Poisson system with subcritical or critical nonlinearities
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DOI: 10.1002/mma.6019
Abstract: In this paper, we are concerned with a class of fractional Schrödinger‐Poisson system involving subcritical or critical nonlinearities. By using the Nehari manifold and variational methods, we obtain the existence and multiplicity of nontrivial solutions. read more here.
Keywords: dinger poisson; fractional schr; critical nonlinearities; poisson system ... See more keywords
Existence and multiplicity of normalized solutions for a class of Schrödinger‐Poisson equations with general nonlinearities
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DOI: 10.1002/mma.6140
Abstract: In this paper, we study the existence and multiplicity of standing waves with prescribed L2 ‐norm Schrödinger‐Poisson equations with general nonlinearities in R3 : i∂tψ+Δψ−κ(|x|−1*|φ|2)ψ+f(ψ)=0, where κ>0 and f is superlinear and satisfies the monotonicity… read more here.
Keywords: dinger poisson; schr dinger; existence multiplicity; equations general ... See more keywords
Multibump solutions for nonlinear Schrödinger‐Poisson systems
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DOI: 10.1002/mma.6211
Abstract: In this paper, we study the following Schrödinger‐Poisson equations: −ε2Δu+V(x)u+K(x)ϕu=|u|p−2u,x∈R3,−ε2Δϕ=K(x)u2,x∈R3, where p∈(4,6) , ε>0 is a parameter and V and K satisfy the critical frequency conditions. By using variational methods and penalization arguments, we show… read more here.
Keywords: dinger poisson; schr dinger; solutions nonlinear; multibump solutions ... See more keywords
Existence and limiting behavior of minimizers for attractive Schrödinger‐Poisson systems with periodic potentials
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DOI: 10.1002/mma.6232
Abstract: We study the constrained minimizing problem of the energy functional related to attractive Schrödinger‐Poisson systems with periodic potentials: I(m)=infE(ϕ):ϕ∈H1(R3),‖ϕ‖L22=m, where E(ϕ):=12∫R3|∇ϕ(x)|2dx+12∫R3V(x)|ϕ(x)|2dx−14∬R3×R3|ϕ(x)|2|ϕ(y)|2|x−y|dxdy−1α+2∫R3|ϕ(x)|α+2dx, with m>0 , α>0 , and V is a continuous periodic potential. We first… read more here.
Keywords: poisson systems; dinger poisson; attractive schr; systems periodic ... See more keywords
On the Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with General Potentials and Super-quadratic Nonlinearity
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DOI: 10.1007/s00009-018-1179-8
Abstract: In this article, we are concerned with the following fractional Schrödinger–Poisson system: $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u+V(x)u+\phi u=f(u)&{} \quad \hbox {in}~\mathbb {R}^{3},\\ (-\Delta )^{t}\phi =u^2&{} \quad \hbox {in}~\mathbb {R}^{3},\\ \end{array} \right. \end{aligned}$$(-Δ)su+V(x)u+ϕu=f(u)inR3,(-Δ)tϕ=u2inR3,where $$03$$2s+2t>3, and $$f\in… read more here.
Keywords: dinger poisson; fractional schr; state solutions; ground state ... See more keywords
A mass- and energy-conserved DG method for the Schrödinger-Poisson equation
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DOI: 10.1007/s11075-021-01139-0
Abstract: We construct, analyze, and numerically validate a class of conservative discontinuous Galerkin (DG) schemes for the Schrödinger-Poisson equation. The proposed schemes all shown to conserve both mass and energy. For the semi-discrete DG scheme the… read more here.
Keywords: poisson equation; schr dinger; dinger poisson; mass energy ... See more keywords
FRACTIONAL SCHRÖDINGER–POISSON SYSTEM WITH SINGULARITY: EXISTENCE, UNIQUENESS, AND ASYMPTOTIC BEHAVIOR
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DOI: 10.1017/s0017089520000099
Abstract: Abstract In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*} where… read more here.
Keywords: schr dinger; dinger poisson; poisson system; system singularity ... See more keywords
Multiple positive solutions for a kind of singular Schrödinger–Poisson system
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DOI: 10.1080/00036811.2018.1491035
Abstract: ABSTRACT In this paper, we discuss the following couple of Schrödinger–Poisson system with singularity: where is a bounded smooth domain with boundary , μ, are parameters, and are constants. The existence and multiplicity of positive… read more here.
Keywords: poisson system; system; dinger poisson; positive solutions ... See more keywords
i-SPin: an integrator for multicomponent Schrödinger-Poisson systems with self-interactions
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DOI: 10.1088/1475-7516/2023/04/053
Abstract: We provide an algorithm and a publicly available code to numerically evolve multicomponent Schrödinger-Poisson (SP) systems with a SO(n) symmetry, including attractive or repulsive self-interactions in addition to gravity. Focusing on the case where the… read more here.
Keywords: self interactions; cosmology; dinger poisson; multicomponent schr ... See more keywords
Infinitely Many Solutions of Schrödinger-Poisson Equations with Critical and Sublinear Terms
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DOI: 10.1155/2019/8453176
Abstract: Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China… read more here.
Keywords: mathematics; dinger poisson; many solutions; infinitely many ... See more keywords