Results 91 to 100 of about 446 (156)

Multiple Normalized Solutions to a Choquard Equation Involving Fractional p-Laplacian in ℝ^N

Fractal and Fractional
In this paper, we study the existence of multiple normalized solutions for a Choquard equation involving fractional p-Laplacian in RN. With the help of variational methods, minimization techniques, and the Lusternik–Schnirelmann category, the existence ...
Xin Zhang, Sihua Liang
doaj   +1 more source

Scattering threshold for the focusing energy-critical generalized Hartree equation

Open Mathematics
This work investigates the asymptotic behavior of energy solutions to the focusing nonlinear Schrödinger equation of Choquard type i∂tu+Δu+∣u∣p−2(Iα*∣u∣p)u=0,p=1+2+αN−2,N≥3.i{\partial }_{t}u+\Delta u+{| u| }^{p-2}\left({I}_{\alpha }* {| u| }^{p})u=0 ...
Almuthaybiri Saleh, Peng Congming, Saanouni Tarek   +2 more
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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

Positive Ground State Solutions for Fractional (p, q)-Laplacian Choquard Equation with Singularity and Upper Critical Exponent

Fractal and Fractional
We prove the existence of a positive ground state solution for a fractional (p,q)-Laplacian Choquard equation that features both a singularity and an upper critical exponent.
Zhenyu Bai, Chuanzhi Bai
doaj   +1 more source

Normalized solutions for the Choquard equation with mass supercritical nonlinearity

, 2022
We consider the nonlinear Choquard equation $$\begin{cases} & - \Delta u = (I_\alpha \ast F(u))F'(u) -\mu u \ \text{in}\ \mathbb{R}^N, & u \in \ H^1(\mathbb{R}^N), \ \int_{\mathbb{R}^N} |u|^2 dx=m, \end{cases} $$ where $\alpha\in(0,N)$, $m>0$ is ...
Xu, Na, Ma, Shiwang
core  

Solutions to discrete nonlinear Kirchhoff–Choquard equations

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

Some existence and uniqueness results for logistic Choquard equation

, 2021
We consider the following doubly nonlocal nonlinear logistic problem driven by the fractional $p$-Laplacian \begin{equation*} \pl u = f(x,u) -\cq ~\text{in}~ \O, ~u=0 ~\text{in}~ \Rn\setminus\O.
Giacomoni, J., Sreenadh, K., Anthal, G. C.   +2 more
core  

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 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

Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

, 2018
Consider nonlinear Choquard ...
Seok Jinmyoung
core   +1 more source