Results 81 to 90 of about 1,785 (116)

Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
doaj   +1 more source

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

Advanced 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

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

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

Singularly Perturbed Fractional Schrödinger Equation Involving a General Critical Nonlinearity

Advanced Nonlinear Studies, 2018
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

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

Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation

, 2008
In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr\"odinger equation in all dimensions based on the recent linear profile decomposition results.
Shao, Shuanglin
core   +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
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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

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