{"title":"亚二次哈密顿椭圆系统的小能量解序列","authors":"","doi":"10.1016/j.aml.2024.109260","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with the following Hamiltonian elliptic system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mover><mrow><mi>b</mi></mrow><mo>→</mo></mover><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>⋅</mi><mo>∇</mo><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>v</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mi>i</mi><mi>n</mi><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mover><mrow><mi>b</mi></mrow><mo>→</mo></mover><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>⋅</mi><mo>∇</mo><mi>v</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>v</mi><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>u</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mi>i</mi><mi>n</mi><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>Under a subquadratic growth condition on the nonlinearity, we establish the existence of a sequence of small energy solutions by using a new critical point theorem for strongly indefinite functional.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sequences of small energy solutions for subquadratic Hamiltonian elliptic system\",\"authors\":\"\",\"doi\":\"10.1016/j.aml.2024.109260\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is concerned with the following Hamiltonian elliptic system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mover><mrow><mi>b</mi></mrow><mo>→</mo></mover><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>⋅</mi><mo>∇</mo><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>v</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mi>i</mi><mi>n</mi><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mover><mrow><mi>b</mi></mrow><mo>→</mo></mover><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>⋅</mi><mo>∇</mo><mi>v</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>v</mi><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>u</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mi>i</mi><mi>n</mi><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>Under a subquadratic growth condition on the nonlinearity, we establish the existence of a sequence of small energy solutions by using a new critical point theorem for strongly indefinite functional.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924002805\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002805","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Sequences of small energy solutions for subquadratic Hamiltonian elliptic system
This paper is concerned with the following Hamiltonian elliptic system Under a subquadratic growth condition on the nonlinearity, we establish the existence of a sequence of small energy solutions by using a new critical point theorem for strongly indefinite functional.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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