1. 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
2. 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