Results 61 to 70 of about 1,674 (89)

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
doaj   +1 more source

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source

On generating functions in additive number theory, II: lower-order terms and applications to PDEs. [PDF]

Math Ann, 2021
Brandes J, Parsell ST, Poulias C, Shakan G, Vaughan RC.   +4 more
europepmc   +1 more source

Vortex Filament Equation for a Regular Polygon in the Hyperbolic Plane. [PDF]

J Nonlinear Sci, 2022
de la Hoz F, Kumar S, Vega L.
europepmc   +1 more source

Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
doaj   +1 more source

Nonlinear Scalar Field Equations with L2 Constraint: Mountain Pass and Symmetric Mountain Pass Approaches

Advanced Nonlinear Studies, 2019
We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in ℝN{\mathbb{R}^{N}} (N≥2{N\geq 2}):
Hirata Jun, Tanaka Kazunaga
doaj   +1 more source

The nonlinear Schrödinger equation on the half-line with homogeneous Robin boundary conditions. [PDF]

Proc Lond Math Soc, 2023
Lee JM, Lenells J.
europepmc   +1 more source

Regularity for critical fractional Choquard equation with singular potential and its applications

Advances in Nonlinear Analysis
We study the following fractional Choquard equation (−Δ)su+u∣x∣θ=(Iα*F(u))f(u),x∈RN,{\left(-\Delta )}^{s}u+\frac{u}{{| x| }^{\theta }}=({I}_{\alpha }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N⩾3N\geqslant 3, s∈12,1s\in \left ...
Liu Senli, Yang Jie, Su Yu
doaj   +1 more source

Singularly Perturbed Fractional Schrödinger Equation Involving a General Critical Nonlinearity

Advanced Nonlinear Studies, 2018
In this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schrödinger problem:
Jin Hua, Liu Wenbin, Zhang Jianjun
doaj   +1 more source

Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation

, 2008
In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr\"odinger equation in all dimensions based on the recent linear profile decomposition results.
Shao, Shuanglin
core   +1 more source