Effect of nonlinear perturbations on second order linear nonoscillatory differential equations
A. Shibuya, Kumamoto University, Kurokami, Kumamoto, Japan E. J. Qualitative Theory of Diff. Equ., No. 34. (2010), pp. 1-16.
T. Tanigawa, Kumamoto University, Kurokami, Kumamoto, Japan
| Communicated by I. Kiguradze. | Received on 2010-01-10 Appeared on 2010-06-10 |
Abstract: The aim of this paper is to show that any second order nonoscillatory linear differential equation can be converted into an oscillating system by applying a sufficiently large nonlinear perturbation. This can be achieved through a detailed analysis of possible nonoscillatory solutions of the perturbed differential equation which may exist when the perturbation is sufficiently small. As a consequence the class of oscillation-generating perturbations is determined precisely with respect to the original nonoscillatory linear equation.
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