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New approach to differential equations with countable impulses |
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| Authors: | Hong-Kun Zhang Jin-Guo Lian Jiong Sun |
| Institution: | Hong-Kun Zhang~1,Jin-Guo Lian~2,Jiong Sun~3 1 Department of Mathematics and Statistics,University of Massachusetts,Amherst,MA 01003,USA 2 Department of Mathematics and Statistics,USA 3 Department of Mathematics,Inner Mongolia University,Hohhot,Inner Mongolia 010021,China |
| Abstract: | 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. |
| Keywords: | countable impulses differential operator hyperbolic Jacobi fields hyperbolicity differential operators |
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