Results 11 to 20 of about 446 (156)
Ground state for Choquard equation with doubly critical growth nonlinearity [PDF]
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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Nodal solutions for the Choquard equation [PDF]
Journal of Functional Analysis, 2016 We consider the general Choquard equations $$ -Δu + u = (I_α\ast |u|^p) |u|^{p - 2} u $$ where $I_α$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + α}{N}, \frac{N + α}{N - 2})$ and minimal action nodal solutions for $p \in (2,\frac{N + α}{N - 2})$.
GHIMENTI, MARCO GIPO +1 more
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Existence of Ground State Solutions for Choquard Equation with the Upper Critical Exponent
Fractal and Fractional, 2023 In this article, we investigate the existence of a nontrivial solution for the nonlinear Choquard equation with upper critical exponent see Equation (6). The Riesz potential in this case has never been studied.
Sarah Abdullah Qadha +2 more
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On Uniqueness for the Generalized Choquard Equation
, 2020 We consider the generalized Choquard equation describing trapped electron gas in three dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. The uniqueness of the minimizers for the case p = 2, i.e.
Georgiev V., Venkov G.
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Soliton dynamics for the generalized Choquard equation
Journal of Mathematical Analysis and Applications, 2014 We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call {\em generalized Choquard equation} where the nonlinear term is $(|x|^{θ-N} * |u|^p)|u|^{p-2}u$.
BONANNO, CLAUDIO +3 more
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Multiple solutions of the quasirelativistic Choquard equation [PDF]
Journal of Mathematical Physics, 2012 We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential.
Melgaard, Michael, Zongo, Frederic D. Y.
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Advances in Nonlinear Analysis, 2020 This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
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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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Infinitely many solutions for nonhomogeneous Choquard equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this paper, we study the following nonhomogeneous Choquard equation \begin{equation*} \begin{split} -\Delta u+V(x)u=(I_\alpha*|u|^p)|u|^{p-2}u+f(x),\qquad x\in \mathbb{R}^N, \end{split} \end{equation*} where $N\geq3,\alpha\in(0,N),p\in \big[\frac{N ...
Tao Wang, Hui Guo
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Existence of positive solutions to the nonlinear Choquard equation with competing potentials
Electronic Journal of Differential Equations, 2018 This article concerns the existence of positive solutions of the nonlinear Choquard equation $$ -\Delta u+a(x)u=b(x)\Big(\frac{1}{|x|}*|u|^2\Big)u,\quad u\in H^{1}({\mathbb R}^3), $$ where the coefficients a and b are positive functions such that
Jun Wang, Mengmeng Qu, Lu Xiao
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