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Missouri University of Science and Technology
Mathematics and Statistics Faculty Research & Creative Works
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Full-Text Articles in Physical Sciences and Mathematics
Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner
Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
Oscillation and nonoscillation properties of second order Sturm-Liouville dynamic equations on time scales — for example, second order self-adjoint differential equations and second order Sturm-Liouville difference equations — have attracted much interest. Here we consider a given homogeneous equation and a corresponding equation with forcing term. We give new conditions implying that the latter equation inherits the oscillatory behavior of the homogeneous equation. We also give new conditions that introduce oscillation of the inhomogeneous equation while the homogeneous equation is nonoscillatory. Finally, we explain a gap in a result given in the literature for the continuous and the discrete case. …
Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner
Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
By means of Riccati transformation techniques we establish some oscillation criteria for the second order Emden-Fowler dynamic equation on a time scale. Such equations contain the classical Emden-Fowler equation as well as their discrete counterparts. The classical oscillation results of Atkinson (in the superlinear case) and Belohorec (in the sublinear case) are extended in this paper to Emden-Fowler dynamic equations on any time scale.