Results 21 to 30 of about 1,353 (146)
Liouville theorems for Hénon type Choquard Equation
Communications on Pure and Applied Analysis, 2023 In this paper, the authors study an equation of Choquard type in \(\mathbb{R} ^{N}\): \[ -\Delta u=\left\vert x\right\vert ^{\alpha}\left\vert u\right\vert ^{p-2} u\int_{\mathbb{R}^{N}}\frac{\left\vert y\right\vert ^{\alpha}\left\vert u(y)\right\vert ^{p}}{\left\vert x-y\right\vert ^{N-\mu}}dy, \] where ...
Dong, Jing, He, Haiyang
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Normalized Ground State Solutions for Nonautonomous Choquard Equations
Frontiers of Mathematics, 2023 In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-Δu-λu=\left(\frac{1}{|x|^μ}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \int_{\mathbb{R}^{N}}|u|^{2}dx=c,\quad u\in H^1(\mathbb{R}^N,\mathbb{R}),$$ where $c>0$, $0< ...
Luo, Huxiao, Wang, Lushun
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Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics [PDF]
, 2013 We consider a semilinear elliptic problem [- \Delta u + u = (I_\alpha \ast \abs{u}^p) \abs{u}^{p - 2} u \quad\text{in (\mathbb{R}^N),}] where (I_\alpha) is a Riesz potential and (p>1).
Moroz, Vitaly, Van Schaftingen, Jean
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Ground state for Choquard equation with doubly critical growth nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this paper we consider nonlinear Choquard equation \begin{equation*} -\Delta u+V(x)u=(I_\alpha*F(u))f(u)\quad {\rm in}\ \mathbb{R}^{N}, \end{equation*} where $V\in C(\mathbb{R}^N)$, $I_\alpha$ denotes the Riesz potential, $f(t)=|t|^{p-2}t+|t|^{q-2}t ...
Fuyi Li +3 more
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Advances in Nonlinear Analysis, 2020 In this paper, we study the singularly perturbed fractional Choquard ...
Yang Zhipeng, Zhao Fukun
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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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Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity
Mathematics, 2019 In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non ...
Huxiao Luo, Shengjun Li, Chunji Li
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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
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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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Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains [PDF]
, 2012 We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schroedinger--Newton equation. We show that for some values of
Agmon +40 more
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