文献类型：期刊文献

英文题名：Explicit solutions of the Dirichlet-Schrodinger problem via the new cylindrical Poisson-Schrodinger kernel method

作者：Qiao, Lei[1]

第一作者：乔蕾

通讯作者：Qiao, L[1]

机构：[1]Henan Univ Econ & Law, Sch Math & Informat Sci, Zhengzhou 450046, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Sch Math & Informat Sci, Zhengzhou 450046, Peoples R China.|[1048425]河南财经政法大学数学与信息科学学院;[10484]河南财经政法大学;

年份：2023

外文期刊名：FORUM MATHEMATICUM

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001000067600001)】；

语种：英文

外文关键词：Cylindrical Schrodinger equation; cylindrical Poisson-Schrodinger kernel; Dirichlet-Schrodinger problem

摘要：In this paper, we study the cylindrical Schrodinger operator and construct a modified cylindrical Poisson-Schrodinger kernel, in analogy to the classical theory of the Laplacian in a strip. A new method expressing explicitly the modified cylindrical Poisson-Schrodinger kernels of any degree is obtained, and a formula expressing the modified cylindrical Poisson-Schrodinger integrals in terms of Nevanlinna-Schrodinger norms is deduced. Applications in the solutions of Dirichlet-Schrodinger problem are described. More specifically, the existence and uniqueness of explicit solutions to the problem mentioned above for the cylindrical Schrodinger equation are obtained. It is shown that our method yields more explicit results than do other methods. Much more challenging geometric configurations, such as a cylinder with a rough base bear new and interesting challenges arising from the lateral boundary conditions. These have-at least to our knowledge-not been addressed before.