Results 51 to 60 of about 1,494,768 (123)

Existence, symmetry, and regularity of ground states of a nonlinear Choquard equation in the hyperbolic space

Advances in Nonlinear Analysis
In this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
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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
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Nodal solutions for the Choquard equation [PDF]

, 2016
We consider the general Choquard equations −Δu+u=(Iα∗|u|^p)|u|^(p−2)u where Iα is a Riesz potential. We construct minimal action odd solutions for p∈((N+α)/N,(N+α)/(N−2)) and minimal action nodal solutions for p∈(2,(N+α)/(N−2)).
Van Schaftingen, Jean, GHIMENTI, MARCO GIPO, Ghimenti, Marco   +2 more
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Ground state for Choquard equation with doubly critical growth nonlinearity [PDF]

, 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 ...
Li, Fuyi, Yongyan Huang, Zhanping Liang, Huang, Yongyan, Fuyi Li, Lei Long, Long, Lei, Liang, Zhanping   +7 more
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Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth

Advances in Nonlinear Analysis
We study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Boundary Value Problems, 2018
By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: (−Δ)psu=λ|u|p−2u+(∫Ω|u|pμ,s∗|x−y|μdy)|u|
Yuling Wang, Yang Yang
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Existence of Multiple Positive Solutions for Choquard Equation with Perturbation [PDF]

, 2020
This paper is concerned with the following Choquard equation with perturbation: where ≥ 3, ∈ (0, ), and 2 − ( / ) < < (2 − )/( − 2). This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation.
Jun Wang, Tao Xie, Lu Xiao
core  

Fractional Generalizations of Filtering Problems and Their Associated Fractional Zakai Equation [PDF]

, 2014
In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering
Nelson, Kenric, Umarov, Sabir, Daum, Fred, Daum, Frederick   +3 more
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Normalized solutions for a fractional $N/s$-Laplacian Choquard equation with exponential critical nonlinearities [PDF]

, 2023
In this paper, we are concerned with the following fractional $N/s$-Laplacian Choquard equation \begin{align*} \begin{cases} (-\Delta)^s_{N/s}u=\lambda |u|^{\frac{N}{s}-2}u +(I_\mu*F(u))f(u),\ \ \mbox{in}\ \mathbb{R}^N, \displaystyle\int_{\mathbb{
Chen, Wenjing, Wang, Zexi
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Normalized solutions for a class of fractional Choquard equations with mixed nonlinearities

Demonstratio Mathematica
In this paper we study the following fractional Choquard equation with mixed nonlinearities:(−Δ)su=λu+αIμ∗|u|q|u|q−2u+Iμ∗|u|p|u|p−2u,x∈RN,∫RN|u|2dx=c2>0.
Chen Shaoxiong, Yang Zhipeng, Zhang Xi
doaj   +1 more source