Results 71 to 80 of about 1,674 (89)

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

Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
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, Rowan Killip, Monica Vişan   +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 elliptic sinh-Gordon equation in a semi-strip

Advances in Nonlinear Analysis, 2017
We study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems.
Hwang Guenbo
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

Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity

Advances in Nonlinear Analysis, 2018
This paper is concerned with the following Kirchhoff-type problem with convolution nonlinearity:
Chen Sitong, Zhang Binlin, Tang Xianhua
doaj   +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

A remark on Gibbs measures with log-correlated Gaussian fields

Forum of Mathematics, Sigma
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, Kihoon Seong, Leonardo Tolomeo   +2 more
doaj   +1 more source

UC and BUC plane partitions

European Physical Journal C: Particles and Fields
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

A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations. [PDF]

Stoch Partial Differ Equ, 2018
Oh T, Thomann L.
europepmc   +1 more source