一类二阶时滞拟线性schrÖdinger方程同斜轨道的存在性

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1216/rmj.2023.53.1489

Chengjun Guo, Baili Chen, Junming Liu, Ravi P. Agarwal

{"title":"一类二阶时滞拟线性schrÖdinger方程同斜轨道的存在性","authors":"Chengjun Guo, Baili Chen, Junming Liu, Ravi P. Agarwal","doi":"10.1216/rmj.2023.53.1489","DOIUrl":null,"url":null,"abstract":"We study the existence of homoclinic orbits of the second order quasilinear Schrödinger equations u¨(t)−V(t)u(t)+2[u¨(t)u2(t)+u˙2(t)u(t)]+g(t,u(t+τ),u(t),u(t−τ))=h(t). containing both advance and retardation terms. By using critical point theory and variational approaches, we establish two different existence results. The first is based on g which does not satisfy the Ambrosetti–Rabinowitz growth condition. The second is based on g satisfying the Ambrosetti–Rabinowitz growth condition.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"2013 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"EXISTENCE OF HOMOCLINIC ORBITS OF A CLASS OF SECOND-ORDER QUASILINEAR SCHRÖDINGER EQUATIONS WITH DELAY\",\"authors\":\"Chengjun Guo, Baili Chen, Junming Liu, Ravi P. Agarwal\",\"doi\":\"10.1216/rmj.2023.53.1489\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the existence of homoclinic orbits of the second order quasilinear Schrödinger equations u¨(t)−V(t)u(t)+2[u¨(t)u2(t)+u˙2(t)u(t)]+g(t,u(t+τ),u(t),u(t−τ))=h(t). containing both advance and retardation terms. By using critical point theory and variational approaches, we establish two different existence results. The first is based on g which does not satisfy the Ambrosetti–Rabinowitz growth condition. The second is based on g satisfying the Ambrosetti–Rabinowitz growth condition.\",\"PeriodicalId\":49591,\"journal\":{\"name\":\"Rocky Mountain Journal of Mathematics\",\"volume\":\"2013 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rocky Mountain Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1216/rmj.2023.53.1489\",\"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":"Rocky Mountain Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1216/rmj.2023.53.1489","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

研究了二阶拟线性Schrödinger方程u¨(t)−V(t)u(t)+2[u¨(t)u2(t)+u˙2(t)u(t)]+g(t,u(t+τ)，u(t−τ)，u(t))=h(t)的同斜轨道的存在性。同时包含提前和延迟条件的。利用临界点理论和变分方法，得到了两个不同的存在性结果。第一种是基于不满足Ambrosetti-Rabinowitz生长条件的g。第二种是基于g满足Ambrosetti-Rabinowitz生长条件。

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

EXISTENCE OF HOMOCLINIC ORBITS OF A CLASS OF SECOND-ORDER QUASILINEAR SCHRÖDINGER EQUATIONS WITH DELAY

We study the existence of homoclinic orbits of the second order quasilinear Schrödinger equations u¨(t)−V(t)u(t)+2[u¨(t)u2(t)+u˙2(t)u(t)]+g(t,u(t+τ),u(t),u(t−τ))=h(t). containing both advance and retardation terms. By using critical point theory and variational approaches, we establish two different existence results. The first is based on g which does not satisfy the Ambrosetti–Rabinowitz growth condition. The second is based on g satisfying the Ambrosetti–Rabinowitz growth condition.

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

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.