Results 41 to 50 of about 1,353 (146)
Perturbation Method for Particle-like Solutions of the Einstein-Dirac-Maxwell Equations [PDF]
, 2009 The aim of this Note is to prove by a perturbation method the existence of solutions of the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state and with the electromagnetic ...
Finster +6 more
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Existence of groundstates for a class of nonlinear Choquard equations [PDF]
, 2012 We prove the existence of a nontrivial solution (u \in H^1 (\R^N)) to the nonlinear Choquard equation [- \Delta u + u = \bigl(I_\alpha \ast F (u)\bigr) F' (u) \quad \text{in (\R^N),}] where (I_\alpha) is a Riesz potential, under almost necessary ...
Jean, Van Schaftingen, Vitaly Moroz
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Singularly perturbed critical Choquard equations
Journal of Differential Equations, 2017 In this paper we study the semiclassical limit for the singularly perturbed Choquard equation $$ -\vr^2 u +V(x)u =\vr^{ -3}\Big(\int_{\R^3} \frac{Q(y)G(u(y))}{|x-y|^ }dy\Big)Q(x)g(u) \quad \mbox{in $\R^3$}, $$ where ...
Alves, Claudianor +3 more
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Choquard equations under confining external potentials [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2016 We consider the nonlinear Choquard equation $$ - u+V u=(I_ \ast \vert u\vert ^p)\vert u\vert ^{p-2}u \qquad \text{ in } \mathbb{R}^N $$ where $N\geq 1$, $I_ $ is the Riesz potential integral operator of order $ \in (0, N)$ and $p > 1$. If the potential $ V \in C (\mathbb{R}^N; [0,+\infty)) $ satisfies the confining condition $$ \liminf\limits_ ...
Jean Van Schaftingen, Jiankang Xia
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Infinitely many non-radial solutions for a Choquard equation
Advances in Nonlinear Analysis, 2022 In this article, we consider the non-linear Choquard equation −Δu+V(∣x∣)u=∫R3∣u(y)∣2∣x−y∣dyuinR3,-\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\
Gao Fashun, Yang Minbo
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Orbital stability of generalized Choquard equation [PDF]
Boundary Value Problems, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xing, Sun, Xiaomei, Lv, Wenhua
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Saddle solutions for the fractional Choquard equation [PDF]
Zeitschrift für angewandte Mathematik und Physik, 2022 We study the saddle solutions for the fractional Choquard equation \begin{align*} (- )^{s}u+ u=(K_ \ast|u|^{p})|u|^{p-2}u, \quad x\in \mathbb{R}^N \end{align*} where $s\in(0,1)$, $N\geq 3$ and $K_ $ is the Riesz potential with order $ \in (0,N)$. For every Coxeter group $G$ with rank $1\leq k\leq N$ and $p\in[2,\frac{N+ }{N-2s})$, we construct a ...
Ying-Xin Cui, Jiankang Xia
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Advances in Nonlinear Analysis, 2019 The paper is concerned with the existence and multiplicity of positive solutions of the nonhomogeneous Choquard equation over an annular type bounded domain.
Goel Divya, Sreenadh Konijeti
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Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities
Advanced Nonlinear Studies, 2021 In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential.
Shen Yansheng
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Multiple solutions for a quasilinear Choquard equation with critical nonlinearity
Open Mathematics, 2021 In the present work, we are concerned with the multiple solutions for quasilinear Choquard equation with critical nonlinearity in RN{{\mathbb{R}}}^{N}.
Li Rui, Song Yueqiang
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