New Approach to Differential Equations with Countable Impulses

This paper provides a new approach to study the solutions of a class of generalized Jazobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n ＋ 1. A new class of generalized differential operators is defined. We investigate the kernel of th...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 27; no. 2; pp. 255 - 262
Main Authors Zhang, Hong-Kun, Lian, Jin-Guo, Sun, Jiong
Format Journal Article
LanguageEnglish
Published Heildeberg Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2011
Subjects
Applications of Mathematics
Jacobi
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Riemann流形
Theoretical
广义微分算子
极大算子
算子理论
线性方程组
脉冲微分方程
37D
countable impulses
hyperbolic
hyperbolicity
differential operators
differential operator
34L
Jacobi fields
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Summary:This paper provides a new approach to study the solutions of a class of generalized Jazobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n ＋ 1. A new class of generalized differential operators is defined. We investigate the kernel of the corresponding maximal operators by applying operator theory. It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic, in which there are n dimension solutions with exponential-decaying amplitude.
Bibliography:countable impulses, differential operator, hyperbolic, Jacobi fields, hyperbolicity, differential operators
O175.8
11-2041/O1
O186.12
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-011-0060-3