Results 71 to 80 of about 2,009 (123)

Scattering threshold for the focusing energy-critical generalized Hartree equation

open access: yesOpen 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   +2 more
doaj   +1 more source

Nonuniqueness of weak solutions of the nonlinear Schroedinger equation [PDF]

open access: yesarXiv, 2005
Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schr\"odinger equation, with certain nonlinearities, are not unique. For any $s<0$ there exist nonzero generalized solutions varying continuously in the Sobolev space $H^s$, with identically vanishing initial data.
arxiv  

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

open access: yesAdvances 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

Spectral Theory and Nonlinear PDE: a Survey [PDF]

open access: yesarXiv, 2005
This is a slightly modified version of the survey article. Minor changes to the text and the references have been made.
arxiv  

Strichartz estimates for the magnetic Schrödinger equation [PDF]

open access: yesarXiv, 2005
We prove global, scale invariant Strichartz estimates for the linear magnetic Schr\"odinger equation with small time dependent magnetic field. This is done by constructing an appropriate parametrix. As an application, we show a global regularity type result for Schr\"odinger maps in dimensions $n\geq 6$.
arxiv  

Rough solutions of a Schroedinger - Benjamin - Ono system [PDF]

open access: yesarXiv, 2005
The Cauchy problem for a coupled Schroedinger and Benjamin - Ono system is shown to be globally well-posed for a class of data without finite energy. The proof uses the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.
arxiv  

Single--peaks for a magnetic Schrödinger equation with critic al growth [PDF]

open access: yesarXiv, 2006
We prove existence results of complex-valued solutions for a semilinear Schr\"odinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory.
arxiv  

Small noise asymptotic of the timing jitter in soliton transmission [PDF]

open access: yesarXiv, 2006
This submission has been withdrawn because it is a duplicate of [math.PR/0609434].
arxiv  

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

open access: yesAdvanced 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

Home - About - Disclaimer - Privacy