非线性不定问题的规定能量鞍点解

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2023-03-04 DOI:10.58997/ejde.2023.23

Y. Il'yasov, E. D. Da Silva, Maxwell Lizete Da Silva

{"title":"非线性不定问题的规定能量鞍点解","authors":"Y. Il'yasov, E. D. Da Silva, Maxwell Lizete Da Silva","doi":"10.58997/ejde.2023.23","DOIUrl":null,"url":null,"abstract":"A minimax variational method for finding mountain pass-type solutions with prescribed energy levels is introduced. The method is based on application of the Linking Theorem to the energy-level nonlinear Rayleigh quotients which critical points correspond to the solutions of the equation with prescribed energy. An application of the method to nonlinear indefinite elliptic problems with nonlinearities that does not satisfy the Ambrosetti-Rabinowitz growth conditions is also presented.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Prescribed energy saddle-point solutions of nonlinear indefinite problems\",\"authors\":\"Y. Il'yasov, E. D. Da Silva, Maxwell Lizete Da Silva\",\"doi\":\"10.58997/ejde.2023.23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A minimax variational method for finding mountain pass-type solutions with prescribed energy levels is introduced. The method is based on application of the Linking Theorem to the energy-level nonlinear Rayleigh quotients which critical points correspond to the solutions of the equation with prescribed energy. An application of the method to nonlinear indefinite elliptic problems with nonlinearities that does not satisfy the Ambrosetti-Rabinowitz growth conditions is also presented.\",\"PeriodicalId\":49213,\"journal\":{\"name\":\"Electronic Journal of Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.58997/ejde.2023.23\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.58997/ejde.2023.23","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

介绍了一种求具有规定能级的山口型解的极大极小变分方法。该方法基于链接定理对能级非线性瑞利商的应用，其中临界点对应于具有规定能量的方程的解。还将该方法应用于不满足Ambrosetti-Rabinowitz增长条件的非线性不定椭圆问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Prescribed energy saddle-point solutions of nonlinear indefinite problems

A minimax variational method for finding mountain pass-type solutions with prescribed energy levels is introduced. The method is based on application of the Linking Theorem to the energy-level nonlinear Rayleigh quotients which critical points correspond to the solutions of the equation with prescribed energy. An application of the method to nonlinear indefinite elliptic problems with nonlinearities that does not satisfy the Ambrosetti-Rabinowitz growth conditions is also presented.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.