{"title":"具有Neumann边界条件的分数阶算子叠加的一些非线性问题","authors":"Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli, Enrico Valdinoci","doi":"10.1002/mana.70006","DOIUrl":null,"url":null,"abstract":"<p>We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order.</p><p>The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well).</p><p>New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a mountain pass method, the other to a linking technique.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2570-2595"},"PeriodicalIF":0.8000,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70006","citationCount":"0","resultStr":"{\"title\":\"Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions\",\"authors\":\"Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli, Enrico Valdinoci\",\"doi\":\"10.1002/mana.70006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order.</p><p>The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well).</p><p>New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a mountain pass method, the other to a linking technique.</p>\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"298 8\",\"pages\":\"2570-2595\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70006\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.70006\",\"RegionNum\":3,\"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":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.70006","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions
We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order.
The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well).
New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a mountain pass method, the other to a linking technique.
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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