临界非线性Schrödinger-Kirchhoff-type方程解的多重性

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-18 DOI:10.1080/00036811.2023.2269967

Jianjun Nie, Quanqing Li

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引用次数: 0

摘要

摘要本文研究了以下临界非线性Schrödinger-Kirchhoff方程:($P$){−(a+b∫RN|∇u|2dx)Δu+V(x)u=P(x)|u|2∗−2u+μ|u|q−2u，在RN中，u∈H1(RN)($P$)其中a,b，μ>0, N≥3,max{2∗−1,2}0和P(x)≥0是两个连续函数。通过变分方法和截断技术，我们证明了方程(P)解的多重性。关键词:Schrödinger-Kirchhoff方程临界指数局部Pohozaev恒等式解的多重性2020数学学科分类:35J1047J30披露声明作者未报告潜在的利益冲突。基金资助:国家自然科学基金项目[批准号12261031,12261076,11801545]和中央高校基本科研业务费专项基金项目[批准号2023MS078]。

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Multiplicity of solutions for a critical nonlinear Schrödinger–Kirchhoff-type equation

AbstractIn this paper, we study the following critical nonlinear Schrödinger–Kirchhoff equation: ($P$) {−(a+b∫RN|∇u|2dx)Δu+V(x)u=P(x)|u|2∗−2u+μ|u|q−2u, in RN,u∈H1(RN)($P$) where a,b,μ>0, N≥3, max{2∗−1,2}0 and P(x)≥0 are two continuous functions. By using the variational method and truncation technique, we prove the multiplicity of solutions for Equation (P).Keywords: Schrödinger–Kirchhoff equationcritical exponentlocal Pohozaev identitiesmultiplicity of solutions2020 Mathematics Subject Classifications: 35J1047J30 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by the National Natural Science Foundation of China [grant numbers 12261031, 12261076, 11801545] and the Fundamental Research Funds for the Central Universities [grant number 2023MS078].

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.