Results 61 to 70 of about 134 (115)

A note on coupled nonlinear Schrödinger equations

Advances in Nonlinear Analysis, 2014
We investigate the initial value problem for some coupled nonlinear Schrödinger equations in two space dimensions with exponential growth. We prove global well-posedness and scattering in the defocusing case. In the focusing sign, existence of non-global
Saanouni Tarek
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Concentration of blow-up solutions for the Gross-Pitaveskii equation

Advances in Nonlinear Analysis
We consider the blow-up solutions for the Gross-Pitaveskii equation modeling the attractive Boes-Einstein condensate. First, a new variational characteristic is established by computing the best constant of a generalized Gagliardo-Nirenberg inequality ...
Zhu Shihui
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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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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Stochastic fluctuations in the Gross-Pitaevskii equation,” Nonlinearity 20

, 2007
We study from a mathematical point of view a model equation for a Bose-Einstein condensation, in the case where the trapping potential varies randomly in time.
Anne De Bouard, Reika Fukuizumi
core  

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
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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

Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent

Advances in Nonlinear Analysis
In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type −Δu+u2∗1∣4πx∣u=μf(x)∣u∣p−2u+g(x)∣u∣4uinR3,-\Delta u+\left({u}^{2}\ast \frac{1}{| 4\pi x| }\right)u=\mu f\left(x){| u| }^{p-2 ...
Zheng Tian-Tian, Lei Chun-Yu, Liao Jia-Feng   +2 more
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Глобални резултати за решението на уравнението на шрьодингер с критична маса и нелинейност от конволюционен тип в R^n

, 2010
Георги Венков, Христо Генев - Разглеждаме един клас от L^2 - критични нелинейни уравнения на Шрьодингер в R^(1+n) с конволюционна нелинейност от тип Хартри.
Genev, Hristo, Venkov, George
core  

Nodal solutions for a zero-mass Chern-Simons-Schrödinger equation

Advances in Nonlinear Analysis
This study deals with the existence of nodal solutions for the following gauged nonlinear Schrödinger equation with zero mass: −Δu+hu2(∣x∣)∣x∣2+∫∣x∣+∞hu(s)su2(s)dsu=∣u∣p−2u,x∈R2,-\Delta u+\left(\frac{{h}_{u}^{2}\left(| x| )}{{| x| }^{2}}+\underset{| x| }{
Deng Yinbin, Liu Chenchen, Yang Xian
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