Results 101 to 110 of about 1,353 (146)

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

Existence of ground state solution for critical N-Laplacian Kirchhoff-type problem with convolution nonlinearity

Bulletin of Mathematical Sciences
In this paper, we investigate the following N-Laplacian Kirchhoff–Choquard-type equation involving the critical exponential growth nonlinearity of Trudinger–Moser-type: −1+b∫ℝN|∇u|NdxΔNu+V(x)|u|N−2u=(|x|−μ∗F(x,u))f(x,u),x∈ℝN,N≥2,u∈W1,N(ℝN), where ...
Lizhen Lai, Dongdong Qin, Die Hu, Jing Zhang   +3 more
doaj   +1 more source

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 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  

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

Multiple solutions for the quasilinear Choquard equation with Berestycki-Lions-type nonlinearities

Advances in Nonlinear Analysis
In this article, we study the following quasilinear equation with nonlocal nonlinearity −Δu−κuΔ(u2)+λu=(∣x∣−μ*F(u))f(u),inRN,-\Delta u-\kappa u\Delta \left({u}^{2})+\lambda u=\left({| x| }^{-\mu }* F\left(u))f\left(u),\hspace{1em}\hspace{0.1em}\text{in ...
Jia Yue, Yang Xianyong
doaj   +1 more source

Existence and nonexistence of nontrivial solutions for Choquard type equations

Electronic Journal of Differential Equations, 2016
In this article, we consider the nonlocal problem $$ -\Delta u+u=q(x)\Big(\int_{\mathbb{R}^N}\frac{q(y)|u(y)|^p}{|x-y|^{N-\alpha}}dy \Big)|u|^{p-2}u,\quad x\in \mathbb{R}^N, $$ where $N\geq 3$, $\alpha\in (0,N)$, $\frac{N+\alpha}{N}
Tao Wang
doaj  

A novel method for approximate solution of two point non local fractional order coupled boundary value problems. [PDF]

PLoS One
Tadoummant L, Khalil H, Echarggaoui R, Aljohani S, Mlaiki N.   +4 more
europepmc   +1 more source

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Saddle solutions for the Choquard equation II

Nonlinear Analysis, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Zhi-Qiang, Xia, Jiankang
openaire   +2 more sources

Quasilinear Choquard equation with critical exponent

Journal of Mathematical Analysis and Applications, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu Su, Hongxia Shi
openaire   +1 more source