{"title":"上半平面非线性高阶方程的 Dirichlet 问题","authors":"Pelin Ayşe Gökgöz","doi":"10.1007/s11785-024-01566-6","DOIUrl":null,"url":null,"abstract":"<p>In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"5 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dirichlet Problem for Nonlinear Higher-Order Equations in Upper Half Plane\",\"authors\":\"Pelin Ayşe Gökgöz\",\"doi\":\"10.1007/s11785-024-01566-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.</p>\",\"PeriodicalId\":50654,\"journal\":{\"name\":\"Complex Analysis and Operator Theory\",\"volume\":\"5 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Analysis and Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11785-024-01566-6\",\"RegionNum\":4,\"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":"Complex Analysis and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01566-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Dirichlet Problem for Nonlinear Higher-Order Equations in Upper Half Plane
In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.
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Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.
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