Results 61 to 70 of about 1,721 (90)

Dispersive estimates and NLS on product manifolds

, 2010
We prove a general dispersive estimate for a Schroedinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates.
Pierfelice, Vittoria
core  

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
doaj   +1 more source

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

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

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
doaj   +1 more source

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

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
doaj   +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

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
doaj   +1 more source