Results 101 to 110 of about 1,216,221 (148)

Odd symmetry of least energy nodal solutions for the Choquard equation

, 2018
We consider the Choquard equation (also known as stationary Hartree equation or Schrödinger–Newton equation) −Δu+u=(Iα⋆|u|p)|u|p−2u.
Ruiz, David, Van Schaftingen, Jean, David Ruiz, Jean Van Schaftingen   +3 more
core   +1 more source

Solutions to discrete nonlinear Kirchhoff–Choquard equations

Bulletin of the Malaysian Mathematical Sciences Society
18 ...
openaire   +2 more sources

Multiple nodal solutions of nonlinear Choquard equations

Electronic Journal of Differential Equations, 2017
In this article, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation $$\displaylines{ -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \quad \text{in }\mathbb{R}^3,\cr u\in H^1(\mathbb{R}^3), }$$ where $p\in (5/2,5 ...
Zhihua Huang, Jianfu Yang, Weilin Yu
doaj  

Normalized ground state solutions for a mass supercritical Choquard equation

Bulletin of Mathematical Sciences
This paper is concerned with the existence of normalized ground state solutions for a class of nonlinear Choquard equations with mass supercritical growth.
Kaizhen Yang, Xianyong Yang
doaj   +1 more source

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
doaj  

Normalized ground states for a kind of Choquard–Kirchhoff equations with critical nonlinearities

Boundary Value Problems
In this paper, we consider the existence of a normalized ground-state solution for the Choquard–Kirchhoff equation: { − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u = λ u + μ ( I α ∗ | u | p ) | u | p − 2 u + ω | u | 4 u , in R 3 , u > 0 , ∫ R 3 | u | 2 = m 2 , in ...
Jiayi Fei, Qiongfen Zhang
doaj   +1 more source

Ground state solutions for Choquard type equations with a singular potential

Electronic Journal of Differential Equations, 2017
This article concerns the Choquard type equation $$ -\Delta u+V(x)u=\Big(\int_{\mathbb{R}^N}\frac{|u(y)|^p}{|x-y|^{N-\alpha}}dy\Big) |u|^{p-2}u,\quad x\in \mathbb{R}^N, $$ where $N\geq3$, $\alpha\in ((N-4)_+,N)$, $2\leq p
Tao Wang
doaj  

Multiple concentrating solutions for a fractional (p, q)-Choquard equation

Advanced Nonlinear Studies
We focus on the following fractional (p, q)-Choquard problem: (−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=1|x|μ*F(u)f(u) in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0 in RN, $\begin{cases}{\left(-{\Delta}\right)}_{p}^{s}u+{\left(-{\Delta}\right)}_{q}^{s}u+V\left(\varepsilon ...
Ambrosio Vincenzo
doaj   +1 more source

Ground state solution for Schrödinger-Choquard equation: doubly critical case

Boundary Value Problems
In this paper, we investigate the following Schrödinger-Choquard equation: − Δ u + u = ( I α ∗ | u | 2 α ♯ ) | u | 2 α ♯ − 2 u + | u | q − 2 u + | u | r − 2 u , x ∈ R N , $$ -\Delta u+u = (I_{\alpha }*|u|^{2_{\alpha }^{\sharp }})|u|^{2_{\alpha }^{ \sharp
Yusheng Shen, Zhiwei Zou, You Gao
doaj   +1 more source

On nonhomogeneous Choquard equation with Hardy–Littlewood–Sobolev critical nonlinearity

Boundary Value Problems
In this paper, we investigate the existence of nontrivial solutions to the following critical nonhomogeneous Choquard equation: { − Δ u = λ u + ∫ Ω ( | u ( y ) | 2 α ∗ | x − y | α d y ) | u | 2 α ∗ − 2 u + f ( x ) i n Ω , u ∈ H 0 1 ( Ω ) , $$ \left ...
Rachid Echarghaoui, Rachid Kouik, Rachid Sersif   +2 more
doaj   +1 more source