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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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 15; no. 5; pp. 912 - 921
Main Authors BUTLER, G. J, SREE HARI RAO, V
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.09.1984
Subjects
Exact sciences and technology
Function theory, analysis
Hypotheses
Inequality
Mathematical functions
Mathematical methods in physics
Ordinary differential equations
Physics
Second order equation
Perturbation
Linear equation
Differential equation
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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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ISSN:0036-1410
1095-7154
DOI:10.1137/0515068