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Full-Text Articles in Mathematics
Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner
Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers, respectively. The approach is mainly based on the Krasnosel'skilatin small letter i with breve fixed point theorem, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales. This study shows …
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.
Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.