Results 71 to 80 of about 1,494,768 (123)

Limit profiles and the existence of bound-states in exterior domains for fractional Choquard equations with critical exponent

Advances in Nonlinear Analysis
This article is devoted to studying the existence of positive solutions to the following fractional Choquard equation: (−Δ)su+u=∫Ω∣u(y)∣p∣x−y∣N−αdy∣u∣p−2u+ε∫Ω∣u(y)∣2α,s*∣x−y∣N−αdy∣u∣2α,s*−2u,inΩ,u=0,onRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+u=
Ye Fumei, Yu Shubin, Tang Chun-Lei
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Existence of ground state solutions for fractional Choquard systems

This article studies the existence of ground state solutions for nonlinear fractional Choquard systems. Under Berestycki-Lions type assumptions on the nonlinearity, we develop a variational framework in fractional Sobolev spaces to tackle the system. The
Yulin Zhao, Hui Xu
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Multiplicity of solutions to a nonlocal Choquard equation involving fractional magnetic operators and critical exponent

Electronic Journal of Differential Equations, 2016
In this article, we study the multiplicity of solutions to a nonlocal fractional Choquard equation involving an external magnetic potential and critical exponent, namely, $$\displaylines{ (a+b[u]_{s,A}^2)(-\Delta)_A^su+V(x)u =\int_{\mathbb{R}^N ...
Fuliang Wang, Mingqi Xiang
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Necessary optimality conditions for fractional action-like problems with intrinsic and observer times [PDF]

, 2008
We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems.
Frederico, G.S.F., Torres, D.F.M.
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Formulation and Solution of Space-Time Fractional KdV-Burgers Equation

, 2013
The space-time fractional KdV-Burgers equation has been derived using the semi-inverse method and Agrawal’s variational method. The modified Riemann-Liouville definition is used for the fractional differential operators.
Abulwafa Essam M.
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Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities

Electronic Journal of Differential Equations, 2019
In this work, we establish the existence of solutions for the nonlinear nonlocal system of equations involving the fractional Laplacian, \begin{gather*} \begin{aligned} (-\Delta)^s u & = au+bv+\frac{2p}{p+q}\int_{\Omega}\frac{|v(y)|^q}{|x-y|^\mu}dy|
Yang Yang, Qian Yu Hong, Xudong Shang
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Multidimensional fractional Schrödinger equation

, 2012
This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form ħ ⁠, with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle.
M. M. Rodrigues, N. Vieira, Vieira, Nelson, Rodrigues, M. M.   +3 more
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Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities

In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem also includes ...
Miyagaki, Olímpio Hiroshi, Siqueira, Rafaella Ferreira dos Santos, Assunção, Ronaldo Brasileiro   +2 more
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Soliton dynamics for the generalized Choquard equation

, 2014
We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call generalized Choquard equation where the nonlinear term is $(|x|^{\theta-N} \star |u|^p) |u|^{p-2}
GHIMENTI, MARCO GIPO, Squassina M., D'Avenia P., BONANNO, CLAUDIO   +3 more
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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
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