Results 11 to 20 of about 320,316 (300)

Normalized solutions for the p-Laplacian equation with a trapping potential

Advances in Nonlinear Analysis, 2023
In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where r=pr=p or 2.2.
Wang Chao, Sun Juntao
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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 multi-bump solutions for saturable Schrödinger equations

Advances in Nonlinear Analysis, 2019
In this paper, we are concerned with the existence of multi-bump solutions for a class of semiclassical saturable Schrödinger equations with an density function:
Wang Xiaoming, Wang Zhi-Qiang
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Normalized solutions for a fractional coupled critical Hartree system [PDF]

Electronic Journal of Qualitative Theory of Differential Equations
We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality.
Shengbing Deng, Wenshan Luo
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Normalized solutions for a coupled Schr\"odinger system [PDF]

Mathematische Annalen, 2020
In the present paper, we prove the existence of solutions $(\lambda_1,\lambda_2,u,v)\in\mathbb{R}^2\times H^1(\mathbb{R}^3,\mathbb{R}^2)$ to systems of coupled Schr\"odinger equations $$ \begin{cases} -\Delta u+\lambda_1u=\mu_1 u^3+\beta uv^2\quad &\hbox{
Zhong, Xuexiu, Bartsch, Thomas, Zou, Wenming   +2 more
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Normalized solutions for critical Schrödinger equations involving (2,q)-Laplacian [PDF]

Opuscula Mathematica
In this paper, we consider the following critical Schrödinger equation involving \((2,q)\)-Laplacian: \[\begin{cases} -\Delta u-\Delta_{q} u=\lambda u+\mu |u|^{\gamma-2}u+|u|^{2^*-2}u \quad\text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N} |u|^{2}dx=a^2,\end{
Lulu Wei, Yueqiang Song
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Non-radial normalized solutions for a nonlinear Schrodinger equation

Electronic Journal of Differential Equations, 2023
This article concerns the existence of multiple non-radial positive solutions of the L2-constrained problem -Δu - Q(ɛx)|u|p-2u = λu, in ℝN, ∫ℝN |u|2dx = 1, where Q(x) is a radially symmetric function, ε>0 is a small parameter, N≥2, and p in (2, 2+4/N)
Zhi-Juan Tong, Jianqing Chen, Zhi-Qiang Wang   +2 more
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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 to Strongly Indefinite Semilinear Equations

Advanced Nonlinear Studies, 2006
In this paper we discuss the existence of normalized solutions of nonlinear elliptic PDEs in gaps of the essential spectrum of the corresponding differential operator.
Maria J Esteban, Eric Sere
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Normalized solutions to Schrödinger systems with potentials

Bulletin of the Iranian Mathematical Society
In this paper, we study the normalized solutions of the Schrödinger system with trapping potentials \begin{equation}\label{eq:diricichlet} \begin{cases} -Δu_1+V_1(x)u_1-λ_1 u_1=μ_1 u_1^3+βu_1u_2^{2}+κu_2~\hbox{in}~ \mathbb{R}^3,\\ -Δu_2+V_2(x)u_2-λ_2 u_2=
Yun, Zhaoyang
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