具有 L2 次临界增长的ℝN 中非线性双谐波薛定谔方程的多重归一化解决方案

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Jun Wang, Li Wang, Ji-xiu Wang
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引用次数: 0

摘要

在本文中,我们考虑了以下非线性双谐波薛定谔方程的归一化解的存在性$$left\{\matrix{{Delta ^2}u = \lambda u + h\left({\varepsilon x} \right)\,f\left(u \right),} &;{x \in \mathbb{R}{^N},} \cr {int_{\mathbb{R}{^N}}{{{left| u \right|}^2}dx = {c^2},}} & {x in\mathbb{R}{^N},} \cr}}\其中 c, ε > 0; N ≥ 5; λ∈ ℝ 是拉格朗日乘数且未知,h∈ C(ℝN; [0;∞)); f: ℝ → ℝ 是满足 L2 次临界增长的连续函数。当 ε 足够小时,我们会得到多个归一化解。此外,我们还得到了解的轨道稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multiple Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in ℝN with L2-Subcritical Growth

In this article, we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations

$$\left\{{\matrix{{{\Delta ^2}u = \lambda u + h\left({\varepsilon x} \right)\,f\left(u \right),} & {x \in \mathbb{R}{^N},} \cr {\int_{\mathbb{R}{^N}} {{{\left| u \right|}^2}dx = {c^2},}} & {x \in \mathbb{R}{^N},} \cr}} \right.$$

where c, ε > 0; N ≥ 5; λ ∈ ℝ is a Lagrange multiplier and is unknown, hC(ℝN; [0;∞)); f: ℝ → ℝ is continuous function satisfying L2-subcritical growth. When ε is small enough, we get multiple normalized solutions. Moreover, we also obtain orbital stability of the solutions.

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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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