一般Kirchhoff型方程正解的唯一性和非退化性

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI:10.1007/s10255-023-1062-7

Yu-ting Kang, Peng Luo, Chang-lin Xiang, Xue-xiu Zhong

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引用次数: 0

摘要

本文研究了广义Kirchhoff型方程$$-M\left(\int_{\mathbb{R}^{N}}{\vert\nabla v\vert}^{2}dx\right)\Delta v=g(v) \quad {\rm in}\;{\mathbb{R}^{N}},$$的唯一性和非退化性，其中M:[0， +∞)∑1是满足若干适当条件的连续函数，且v∈H1(1)。将我们的结果应用于M(t) = at + b, a, b ＆gt；0，我们明确了所有维度N≥1的所有正解。我们的结果可以看作是Li等人的相应结果的推广[JDE， 2020, 268, Section 1.2]。

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Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations

In the present paper, we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations

$$-M\left(\int_{\mathbb{R}^{N}}{\vert\nabla v\vert}^{2}dx\right)\Delta v=g(v) \quad {\rm in}\;{\mathbb{R}^{N}},$$

where M: [0, +∞) ↦ ℝ is a continuous function satisfying some suitable conditions and v ∈ H¹(ℝ^N). Applying our results to the case M(t) = at + b, a, b > 0, we make it clear all the positive solutions for all dimensions N ≥ 1. Our results can be viewed as a generalization of the corresponding results of Li et al. [JDE, 2020, 268, Section 1.2].

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

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.