Results 11 to 20 of about 7,704,118 (361)

Normalized solutions for Kirchhoff-Carrier type equation

AIMS Mathematics, 2023
In this paper, we study the following Kirchhoff-Carrier type equation $ -\left(a+bM\left(|\nabla u|_{2}, |u|_{\tau}\right)\right)\Delta u-\lambda u = |u|^{p-2}u, \quad \ {\rm in}\ \mathbb{R}^{3}, $ where $ a, \ b > 0 $ are constants ...
Jie Yang, Haibo Chen
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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 ...
Thomas Bartsch, Louis Jeanjean
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Normalized solutions for Sobolev critical fractional Schrödinger equation

Advances in Nonlinear Analysis
In the present study, we investigate the existence of the normalized solutions to Sobolev critical fractional Schrödinger equation: (−Δ)su+λu=f(u)+∣u∣2s*−2u,inRN,(Pm)∫RN∣u∣2dx=m2,\hspace{14em}\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+\lambda u=f ...
Li Quanqing, Nie Jianjun, Wang Wenbo, Zhou Jianwen   +3 more
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Normalized solutions for the double-phase problem with nonlocal reaction

Advances in Nonlinear Analysis
In this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and ...
Cai Li, Zhang Fubao
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Normalized solutions for a nonlinear Dirac equation [PDF]

Journal of Differential Equations, 2023
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 ...
V. Coti Zelati, M. Nolasco
semanticscholar   +4 more sources

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, 2023
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, Louis Jeanjean, Nicola Soave   +3 more
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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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Normalized solutions for the Choquard equations with critical nonlinearities

Advances in Nonlinear Analysis
This study is concerned with the existence of normalized solutions for the Choquard equations with critical nonlinearities −Δu+λu=f(u)+(Iα∗∣u∣2α*)∣u∣2α*−2u,inRN,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}-\Delta u+\lambda u=f\left(u)+\left({I}_{\alpha }\ast ...
Gao Qian, He Xiaoming
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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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