{"title":"分数薛定谔-泊松系统的无限多负能量解","authors":"Anbiao Zeng, Guangze Gu","doi":"10.1016/j.aml.2024.109389","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the following fractional Schrödinger–Poisson system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mi>ϕ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>ϕ</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is a fixed constant, <span><math><mi>f</mi></math></span> is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109389"},"PeriodicalIF":2.9000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems\",\"authors\":\"Anbiao Zeng, Guangze Gu\",\"doi\":\"10.1016/j.aml.2024.109389\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider the following fractional Schrödinger–Poisson system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mi>ϕ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>ϕ</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is a fixed constant, <span><math><mi>f</mi></math></span> is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"162 \",\"pages\":\"Article 109389\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-11-22\",\"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/S0893965924004099\",\"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/S0893965924004099","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems
We consider the following fractional Schrödinger–Poisson system where is a fixed constant, is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.
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.