Results 31 to 40 of about 446 (156)
The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate [PDF]
, 2017 We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation and we establish its nondegeneracy.
Cingolani S. +2 more
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The Existence of Normalized Solutions for a Nonlocal Problem in ℝ3
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In this paper, we study the following fractional Schrödinger equation in ℝ3(−Δ)σu − λu = |u|p−2u, in ℝ3 with σ ∈ (0, 1), λ ∈ ℝ and p ∈ (2 + σ, 2 + (4/3)σ). By using the constrained variational method, we show the existence of solutions with prescribed L2 norm for this problem.
Jing Yang, Dimitrios Tsimpis
wiley +1 more source
An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term −div(g2(u)∇u) + g(u)g′(u)|∇u|2 + V(x)u = λ[|x|−μ∗|u|p]|u|p−2u, x ∈ ℝN, where N ≥ 3, g : ℝ → ℝ+ is a C1 even function, g(0) = 1, g′(s) ≥ 0 is for all s ≥ 0, lim∣s∣→+∞gs/sα−1≔β>0 is for some α > 1, and (α − 1)g(s) ≥ g′(s)s is for all s ≥ 0, 2α ≤ p ...
Quanqing Li +4 more
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Choquard equations with critical nonlinearities [PDF]
Communications in Contemporary Mathematics, 2019 In this paper, we study the Brezis–Nirenberg type problem for Choquard equations in [Formula: see text] [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] are the critical exponents in the sense of Hardy–Littlewood–Sobolev inequality and [Formula: see text] is the Riesz ...
Li, Xinfu, Ma, Shiwang
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Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations −Δu+V1xu=Iα∗uN+α/Nuα/N−1u+λv,x∈ℝN,−Δv+V2xv=Iα∗vN+α/Nvα/N−1v+λu,x∈ℝN,u,v∈H1ℝN, are proved, where α ∈ (0, N), N ≥ 3, V1(x)V2(x) ∈ L∞(ℝN) are positive functions, and Iα denotes the Riesz potential.
Huiling Wu, Jacopo Bellazzini
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A Note on a Damped Focusing Inhomogeneous Choquard Equation [PDF]
Zurnal matematiceskoj fiziki, analiza, geometrii, 2021 Summary: This paper is devoted to the focusing inhomogeneous Choquard equation with linear damping: \[ i\dot{u}+\Delta u+iau=-|x|^{-\gamma} (I_\alpha \ast |u|^{p}) |u|^{p-2} u\quad \text{on } \mathbb{R}^N, \] where \(a \geq 0\) and \(0 < \gamma < \operatorname{inf}(N, 2 + \alpha)\).
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Advances in Nonlinear Analysis, 2020 In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard ...
Binhua Feng, Chen Ruipeng, Liu Jiayin
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On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=00,v= on ∂Ω,where Ω ⊂ ℝN is a bounded domain with a smooth boundary, 0 < α < N, 0 < β < N, and F is the primitive of f, similarly for G.
Wenbo Wang +3 more
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Existence of Multiple Positive Solutions for Choquard Equation with Perturbation [PDF]
, 2020 This paper is concerned with the following Choquard equation with perturbation: where ≥ 3, ∈ (0, ), and 2 − ( / ) < < (2 − )/( − 2). This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation.
Jun Wang, Tao Xie, Lu Xiao
core
Boundary Value Problems, 2020 In this paper, we study the following Choquard type quasilinear Schrödinger equation: − Δ u + u − Δ ( u 2 ) u = ( I α ∗ G ( u ) ) g ( u ) , x ∈ R N , $$ -\Delta u+u-\Delta \bigl(u^{2}\bigr)u=\bigl(I_{\alpha }*G(u) \bigr)g(u),\quad x\in {\mathbb{R}}^{N}, $
Yu-bo He, Jue-liang Zhou, Xiao-yan Lin
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