Results 61 to 70 of about 1,705 (80)
Regularity for critical fractional Choquard equation with singular potential and its applications
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
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
Singularly Perturbed Fractional Schrödinger Equation Involving a General Critical Nonlinearity
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
Global solutions to 3D quadratic nonlinear Schrödinger-type equation
We consider the Cauchy problem to the 3D fractional Schrödinger equation with quadratic interaction of $u\bar u$ type. We prove the global existence of solutions and scattering properties for small initial data.
Zihua Guo, Naijia Liu, Liang Song
doaj +1 more source
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 +2 more
doaj +1 more source
Nodal solutions for a zero-mass Chern-Simons-Schrödinger equation
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
Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths +2 more
doaj +1 more source
We establish the well-posedness theory for the quintic nonlinear Schrödinger equation (NLS) on four-dimensional tori (i.e., T4 ${\mathbb{T}}^{4}$ ), which is an energy-supercritical model. Compared to the recent breakthrough work (B. Kwak and S.
Wang Han +4 more
doaj +1 more source
A remark on Gibbs measures with log-correlated Gaussian fields
We study Gibbs measures with log-correlated base Gaussian fields on the d-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson’s argument.
Tadahiro Oh +2 more
doaj +1 more source
This paper is concerned with the investigation of UC and BUC plane partitions based upon the fermion calculus approach. We construct generalized the vertex operators in terms of free charged fermions and neutral fermions and present the interlacing ...
Shengyu Zhang, Zhaowen Yan
doaj +1 more source

