1Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN37403, USA. E-mail: Boris-Belinskiy@utc.edu
2Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN37403, USA. E-mail: John-Graef@utc.edu
3Department of Mathematics, University of Kentucky, Lexington, KY40506, USA. E-mail: petrovic@ms.uky.edu
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.
Comparison theorem, dynamic equations, nonoscillation, oscillation, Sturm–Picone theorem, time scales.
