1. CMB 2014 (vol 58 pp. 174)
|Periodic Solutions of Almost Linear Volterra Integro-dynamic Equation on Periodic Time Scales|
Using Krasnoselskii's fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this papers are new for the continuous and discrete time scales.
Keywords:Volterra integro-dynamic equation, time scales, Krasnoselsii's fixed point theorem, periodic solution
2. CMB 2011 (vol 55 pp. 214)
|Positive Solutions of Impulsive Dynamic System on Time Scales|
In this paper, some criteria for the existence of positive solutions of a class of systems of impulsive dynamic equations on time scales are obtained by using a fixed point theorem in cones.
Keywords:time scale, positive solution, fixed point, impulsive dynamic equation
3. CMB 2008 (vol 51 pp. 161)
|Wirtinger's Inequalities on Time Scales |
This paper is devoted to the study of Wirtinger-type inequalities for the Lebesgue $\Delta$-integral on an arbitrary time scale $\T$. We prove a general inequality for a class of absolutely continuous functions on closed subintervals of an adequate subset of $\T$. By using this expression and by assuming that $\T$ is bounded, we deduce that a general inequality is valid for every absolutely continuous function on $\T$ such that its $\Delta$-derivative belongs to $L_\Delta^2([a,b)\cap\T)$ and at most it vanishes on the boundary of $\T$.
Keywords:time scales calculus, $\Delta$-integral, Wirtinger's inequality