Search

Your search keyword '"Zhu, Xincai"' showing total 6 results
Start Over Author "Zhu, Xincai" Search Limiters Full Text
6 results on '"Zhu, Xincai"'

1. Mass Concentration and Local Uniqueness of Ground States for $L^2$-subcritical Nonlinear Schr\'{o}dinger Equations

Author

Li, Shuai and Zhu, Xincai

Subjects
Mathematics - Analysis of PDEs, 35J50, 35Q40, 46N50
Abstract

We consider ground states of $L^2$-subcritical nonlinear Schr\"{o}dinger equation (1.1), which can be described equivalently by minimizers of the following constraint minimization problem $$ e(\rho):=\inf\{E_{\rho}(u):u\in \mathcal{H}(\mathbb{R}^d),\|u\|_2^2=1\}.$$ The energy functional $E_{\rho}(u)$ is defined by $$ E_{\rho}(u):=\frac{1}{2}\int_{\mathbb{R}^d}|\nabla u|^2dx +\frac{1}{2}\int_{\mathbb{R}^d}V(x)|u|^2dx-\frac{\rho^{p-1}}{p+1}\int_{\mathbb{R}^d}|u|^{p+1}dx,$$ where $d\geq1$, $\rho>0$, $p\in\big(1, 1+\frac{4}{d}\big)$ and $0\leq V(x)\to\infty$ as $|x| \to\infty$. We present a detailed analysis on the concentration behavior of ground states as $\rho\to\infty$, which extends the concentration results shown in [22]. Moreover, the uniqueness of nonnegative ground states is also proved when $\rho$ is large enough.

Published
2018

2. Existence and limit behavior of constraint minimizers for elliptic equations with two nonlocal terms.

Author

Zhu, Xincai and Zhu, Yajie

Subjects
*ELLIPTIC equations, *EXISTENCE theorems, *CONSTRAINT databases, *GENERALIZATION, *MATHEMATICAL analysis
Abstract

This paper is devoted to studying constraint minimizers for a class of elliptic equations with two nonlocal terms. Using the methods of constrained variation and energy estimation, we analyze the existence, non-existence, and limit behavior of minimizers for the related minimization problem. Our work extends and enriches the study of bi-nonlocal problems. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

3. Blow-Up Analysis of L 2 -Norm Solutions for an Elliptic Equation with a Varying Nonlocal Term.

Author

Zhu, Xincai and He, Chunxia

Subjects
*ELLIPTIC equations
Abstract

This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of L 2 -norm solutions for the related equation when the potential function V (x) fulfills an appropriate choice. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

4. Existence and Limit Behavior of Constraint Minimizers for a Varying Non-Local Kirchhoff-Type Energy Functional.

Author

Zhu, Xincai and Wu, Hanxiao

Subjects
*BEHAVIORAL assessment
Abstract

In this paper, we study the constrained minimization problem for an energy functional which is related to a Kirchhoff-type equation. For s = 1 , there many articles have analyzed the limit behavior of minimizers when η > 0 as b → 0 + or b > 0 as η → 0 + . When the equation involves a varying non-local term ∫ R 3 | ∇ u | 2 d x s , we give a detailed limit behavior analysis of constrained minimizers for any positive sequence { η k } with η k → 0 + . The present paper obtains an interesting result on this topic and enriches the conclusions of previous works. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

5. Asymptotic Behavior of Normalized Solutions for Fractional $L^2$-Critical Schrödinger Equations with a Spatially Decaying Nonlinearity

Author

Zhang, Shu and Zhu, Xincai

Subjects
Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)
Abstract

This paper is devoted to studying the following fractional $L^2$-critical nonlinear Schr\"odinger equation $$(-\Delta)^{s} u(x)+V(x)u(x)-a|x|^{-b}|u|^{\frac{4s-2b}{N}}u(x) = \mu u(x)\,\ \hbox{in}\,\ \mathbb{R}^N,$$ where $\mu\in\mathbb{R}$, $a>0$, $s\in(\frac{1}{2},1)$, $N>2s$, $00$ such that (1.4) has minimizers for $0a^*$. For the case of $a=a^*$, it gives a fact that the existence and non-existence of minimizers depend strongly on the value of $V(0)$. Especially for $V(0)=0$, we prove that minimizers occur blow-up behavior and the mass of minimizers concentrates at the origin as $a\nearrow a^*$. Applying implicit function theorem, the uniqueness of minimizers is also proved for $a>0$ small enough.

Published
2023
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results