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A nonlinear Sturm-Picone comparison theorem for dynamic equations on time scales.(Report)
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Abstract
The authors derive an analog of the well-known Picone identity but for nonlinear dynamic equations on time scales. As a consequence, they obtain a nonlinear comparison theorem in the spirit of the classical Sturm-Picone comparison theorem. Comparison results yielding the nonoscillation of all solutions of nonlinear equations are also obtained.
AMS subject classification: 34C10, 34C15, 39A11.
Keywords: Comparison theorem, dynamic equations, nonoscillation, oscillation, Sturm-Picone theorem, time scales.
1. Introduction
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