{"title":"具有可饱和非线性和频谱 0 的周期性薛定谔晶格系统的基态孤子","authors":"Guanwei Chen, Shiwang Ma","doi":"10.1007/s13324-024-00936-9","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with a class of periodic Schrödinger lattice systems with spectrum 0 and saturable nonlinearities. The existence of ground state solitons of the systems under weak assumptions is obtained. The main novelties are as follows. (1) Some new sufficient conditions for the existence of ground state solitons under the “spectral endpoint” assumption are constructed. (2) Our “non-monotonic” conditions make the proofs of the boundedness of the (<i>PS</i>) sequences to be easier. (3) Our result extends and improves the related results in the literature. Besides, some examples are given to illuminate our result.\n</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 4","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0\",\"authors\":\"Guanwei Chen, Shiwang Ma\",\"doi\":\"10.1007/s13324-024-00936-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is concerned with a class of periodic Schrödinger lattice systems with spectrum 0 and saturable nonlinearities. The existence of ground state solitons of the systems under weak assumptions is obtained. The main novelties are as follows. (1) Some new sufficient conditions for the existence of ground state solitons under the “spectral endpoint” assumption are constructed. (2) Our “non-monotonic” conditions make the proofs of the boundedness of the (<i>PS</i>) sequences to be easier. (3) Our result extends and improves the related results in the literature. Besides, some examples are given to illuminate our result.\\n</p></div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"14 4\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13324-024-00936-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00936-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0
This paper is concerned with a class of periodic Schrödinger lattice systems with spectrum 0 and saturable nonlinearities. The existence of ground state solitons of the systems under weak assumptions is obtained. The main novelties are as follows. (1) Some new sufficient conditions for the existence of ground state solitons under the “spectral endpoint” assumption are constructed. (2) Our “non-monotonic” conditions make the proofs of the boundedness of the (PS) sequences to be easier. (3) Our result extends and improves the related results in the literature. Besides, some examples are given to illuminate our result.
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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