Results 81 to 90 of about 3,496 (115)

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

Existence and Asymptotic Behavior of Positive Solutions for a Class of Quasilinear Schrödinger Equations

Advanced Nonlinear Studies, 2018
In this paper, we study the quasilinear Schrödinger equation -Δ⁢u+V⁢(x)⁢u-γ2⁢(Δ⁢u2)⁢u=|u|p-2⁢u{-\Delta u+V(x)u-\frac{\gamma}{2}(\Delta u^{2})u=|u|^{p-2}u}, x∈ℝN{x\in\mathbb{R}^{N}}, where V⁢(x):ℝN→ℝ{V(x):\mathbb{R}^{N}\to\mathbb{R}} is a given potential,
Wang Youjun, Shen Yaotian
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

The Kato smoothing effect for Schr{ö}dinger equations with unbounded potentials in exterior domains [PDF]

arXiv, 2006
In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.
arxiv  

Ground-State Energy of a Dilute Fermi Gas

, 2005
Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials.
Lieb, Elliott H., Seiringer, Robert, Solovej, Jan Philip   +2 more
core   +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 nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential

Advances in Nonlinear Analysis, 2017
Many existence and nonexistence results are known for nonnegative radial solutions to the ...
Rolando Sergio
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

Orbital stability of standing wave solution for a quasilinear Schrödinger equation [PDF]

arXiv, 2007
Via minimization arguments and Concentration Compactness Principle, we prove the orbital stability of standing wave solutions for a class of quasilinear Schr\"{o}dinger equation arising from physics.
arxiv  

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