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
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