{"title":"具有对数扰动和多值对流的各向异性双相椭圆包体系统","authors":"Shengda Zeng, Yasi Lu, Vicenţiu D. Rădulescu","doi":"10.1007/s00245-025-10278-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate a class of variable exponent double phase elliptic inclusion systems involving anisotropic partial differential operators with logarithmic perturbation as well as two fully coupled multivalued terms, one of them is defined in the domain and the other is defined on the boundary, respectively. Firstly, under the suitable coercive conditions, the existence of a weak solution for the double phase elliptic inclusion systems is verified via applying a surjectivity theorem concerning multivalued pseudomonotone operators. Then, when the elliptic inclusion system is considered in non-coercive framework, we employ the sub-supersolution method to establish the existence and compactness results. Finally, we deliver several solvability properties of some special cases with respect to the elliptic inclusion system under consideration via constructing proper sub- and super-solutions.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10278-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Anisotropic Double Phase Elliptic Inclusion Systems with Logarithmic Perturbation and Multivalued Convections\",\"authors\":\"Shengda Zeng, Yasi Lu, Vicenţiu D. Rădulescu\",\"doi\":\"10.1007/s00245-025-10278-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate a class of variable exponent double phase elliptic inclusion systems involving anisotropic partial differential operators with logarithmic perturbation as well as two fully coupled multivalued terms, one of them is defined in the domain and the other is defined on the boundary, respectively. Firstly, under the suitable coercive conditions, the existence of a weak solution for the double phase elliptic inclusion systems is verified via applying a surjectivity theorem concerning multivalued pseudomonotone operators. Then, when the elliptic inclusion system is considered in non-coercive framework, we employ the sub-supersolution method to establish the existence and compactness results. Finally, we deliver several solvability properties of some special cases with respect to the elliptic inclusion system under consideration via constructing proper sub- and super-solutions.</p></div>\",\"PeriodicalId\":55566,\"journal\":{\"name\":\"Applied Mathematics and Optimization\",\"volume\":\"92 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00245-025-10278-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00245-025-10278-y\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10278-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Anisotropic Double Phase Elliptic Inclusion Systems with Logarithmic Perturbation and Multivalued Convections
In this paper, we investigate a class of variable exponent double phase elliptic inclusion systems involving anisotropic partial differential operators with logarithmic perturbation as well as two fully coupled multivalued terms, one of them is defined in the domain and the other is defined on the boundary, respectively. Firstly, under the suitable coercive conditions, the existence of a weak solution for the double phase elliptic inclusion systems is verified via applying a surjectivity theorem concerning multivalued pseudomonotone operators. Then, when the elliptic inclusion system is considered in non-coercive framework, we employ the sub-supersolution method to establish the existence and compactness results. Finally, we deliver several solvability properties of some special cases with respect to the elliptic inclusion system under consideration via constructing proper sub- and super-solutions.
期刊介绍:
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.