Results 11 to 20 of about 8,131,330 (355)

The existence and multiplicity of the normalized solutions for fractional Schrödinger equations involving Sobolev critical exponent in the L2-subcritical and L2-supercritical cases

Advances in Nonlinear Analysis, 2022
This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P)(−Δ)su+λu=μ∣u∣p−2u+∣u∣2s∗−2u,x∈RN,u>0,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}{\left(-\Delta )}^{s}u+\lambda
Li Quanqing, Zou Wenming
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Normalized solutions of L 2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities [PDF]

Nonlinearity, 2022
In this paper we are concerned with the existence of normalized solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities.
Jack Borthwick, Xiaojun Chang, L. Jeanjean, Nicola Soave   +3 more
semanticscholar   +3 more sources

Normalized solutions for nonlinear Schrödinger systems [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017
We consider the existence of normalized solutions in H1(ℝN) × H1(ℝN) for systems of nonlinear Schr¨odinger equations, which appear in models for binary mixtures of ultracold quantum gases. Making a solitary wave ansatz, one is led to coupled systems of elliptic equations of the formand we are looking for solutions satisfyingwhere a1> 0 and a2> 0 ...
Bartsch, Thomas, Jeanjean, Louis
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Normalized solutions for the discrete Schrödinger equations

Boundary Value Problems, 2023
In the present paper, we consider the existence of solutions with a prescribed l 2 $l^{2}$ -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f ( u k ) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , $$ \textstyle\begin{cases} -\Delta ...
Qilin Xie, Huafeng Xiao
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Multiplicity and concentration of normalized solutions for a Kirchhoff type problem with $ L^2 $-subcritical nonlinearities

Communications in Analysis and Mechanics
In this paper, we studied the existence of multiple normalized solutions to the following Kirchhoff type equation:$ \begin{equation*} \begin{cases} -\left(a\varepsilon^2+b\varepsilon\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+V(x)u = \mu u+f(u) &
Yangyu Ni, Jijiang Sun, Jianhua Chen
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Normalized solutions for the Klein–Gordon–Dirac system

Rendiconti Lincei, Matematica e Applicazioni, 2023
We prove the existence of a stationary solution for the system describing the interaction between an electron coupled with a massless scalar field (a photon). We find a solution, with fixed L^2 -norm, by variational methods, as a critical point of an energy functional.
Coti Zelati V., Nolasco M.
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Normalized solutions for logarithmic Schrödinger equation with a perturbation of power law nonlinearity

Annales Fennici Mathematici, 2023
We study the existence of normalized solutions to the following logarithmic Schrödinger equation   \(-\Delta u+\lambda u=\alpha u\log u^2+\mu|u|^{p-2}u\), \(x\in\mathbb{R}^N\),   under the mass constraint   \(\int_{\mathbb{R}^N}u^2\,\mathrm{d}x=c^2\
W. Shuai, Xiaolong Yang
semanticscholar   +3 more sources

Multiplicity of Normalized Solutions to a Fractional Logarithmic Schrödinger Equation

Fractal and Fractional
We study the existence and multiplicity of normalized solutions to the fractional logarithmic Schrödinger equation (−Δ)su+V(ϵx)u=λu+ulogu2inRN, under the mass constraint ∫RN|u|2dx=a.
Yan-Cheng Lv, Gui-Dong Li
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Normalized solutions for a nonlinear Dirac equation

Journal of Differential Equations
We prove the existence of a normalized, stationary solution $Ψ\colon \mathbb{R}^{3} \to \mathbb{C}^{4}$ with frequency $w > 0$ of the nonlinear Dirac equation. The result covers the case in which the nonlinearity is the gradient of a function of the form \begin{equation*} F(Ψ) = a|(Ψ, γ^{0}Ψ)|^{\fracα{2}} + b|(Ψ, γ^{1}γ^{2} γ^{3} Ψ)|^{\fracα{2 ...
Coti Zelati, Vittorio, Nolasco, Margherita   +1 more
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Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians

Advanced Nonlinear Studies, 2022
The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
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