Results 11 to 20 of about 1,353 (146)
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 ...
Adams R. A. +7 more
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Nodal solutions for the Choquard equation [PDF]
Journal of Functional Analysis, 2016 We consider the general Choquard equations $$ -\Delta u + u = (I_\alpha \ast |u|^p) |u|^{p - 2} u $$ where $I_\alpha$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + \alpha}{N}, \frac{N + \alpha}{N - 2})$ and ...
Ghimenti, Marco, Van Schaftingen, Jean
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Choquard equations with mixed potential
Partial Differential Equations and Applications, 2023 In this paper, we study the following class of nonlinear Choquard equation, $$- u+a(z)u=K(u)f(u)\quad \text{in}\quad \R^N,$$ where $\R^N=\R^L\times\R^M$, $L\geq2$, $K(u)=|.|^{- }*F(u)$, $ \in(0,N)$, $a$ is a continuous real function and $F$ is the primitive function of $f$. Under some suitable assumptions mixed on the potential $a$.
Romildo N. de Lima, Marco A. S. Souto
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Boundary Value Problems for Choquard Equations
Nonlinear Analysis, 2023 We prove existence of a positive radial solution to the Choquard equation $$-Δu +V u=(I_α\ast |u|^p)|u|^{p-2}u\qquad\text{in}\,\,\,Ω$$ with Neumann or Dirichlet boundary conditions, when $Ω$ is an annulus, or an exterior domain of the form $\mathbb{R}^N\setminus \bar{B}_a(0)$.
Bernardini C., Cesaroni A.
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On fractional Choquard equations [PDF]
Mathematical Models and Methods in Applied Sciences, 2015 We investigate a class of nonlinear Schrödinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.
D'AVENIA, Pietro +2 more
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Fractional Choquard equation with critical nonlinearities [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2017 In this article, we study the Brezis-Nirenberg type problem of nonlinear Choquard equation involving a fractional Laplacian \[ (-\De)^s u = \left( \int_{\Om}\frac{|u|^{2^*_{ ,s}}}{|x-y|^ }\mathrm{d}y \right)|u|^{2^*_{ ,s}-2}u +\la u \; \text{in } \Om,\] where $\Om $ is a bounded domain in $\mathbb R^n$ with Lipschitz boundary, $\la $ is a real ...
Mukherjee, T., Sreenadh, K.
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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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Multiple solutions for nonhomogeneous Choquard equations
Electronic Journal of Differential Equations, 2018 In this article, we consider the multiple solutions for the nonhomogeneous Choquard equations $$ - \Delta u +u=\Big(\frac{1}{|x|^{\alpha}}\ast |u|^{p}\Big)|u|^{p-2}u+h(x), \quad x\in \mathbb{R}^N, $$ and $$ - \Delta u=\Big(\frac{1}{|x|^{\alpha ...
Lixia Wang
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Ground State Solutions of Fractional Choquard Problems with Critical Growth
Fractal and Fractional, 2023 In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained.
Jie Yang, Hongxia Shi
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Generalized Choquard Equations Driven by Nonhomogeneous Operators [PDF]
Mediterranean Journal of Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Claudianor O. Alves +2 more
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