New approach to differential equations with countable impulses

作者：Zhang, Hong-Kun^*; Lian, Jin-Guo; Sun, Jiong

来源：Acta Mathematicae Applicatae Sinica-English Series, 2011, 27(2): 255-262.

DOI：10.1007/s10255-011-0060-3

• countable impulses
• differential operator
• hyperbolic
• Jacobi fields
• hyperbolicity
• differential operators

This paper provides a new approach to study the solutions of a class of generalized Jacobi 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.

• 出版日期2011-4
• 单位内蒙古大学