Some properties of second order linear differential equations and perturbations that preserve them
We consider perturbations of linear second order ordinary differential equations that preserve certain properties of solutions. In particular, under the assumption that all solutions of the basic equation lie in a certain function space, we find conditions on forced perturbations that maintain the p...
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Published in | SIAM journal on mathematical analysis Vol. 15; no. 5; pp. 912 - 921 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.09.1984
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Subjects | |
Online Access | Get full text |
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Summary: | We consider perturbations of linear second order ordinary differential equations that preserve certain properties of solutions. In particular, under the assumption that all solutions of the basic equation lie in a certain function space, we find conditions on forced perturbations that maintain the property that at most one solution is nonoscillatory. Under the assumption that all solutions of the basic equation are bounded and lie in a certain $L^p $ space, we characterize those $L^k $ linear perturbations that preserve this property. Results of Atkinson, Grimmer and Patula (Ann. Math. Pura Appl., 126 (1980), pp. 296-323), and Patula and Wong (Math. Ann., 197 (1972), pp. 9-28) are extended. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0036-1410 1095-7154 |
DOI: | 10.1137/0515068 |