[PDF] Top 20 Boundedness in functional dynamic equations on time scales

... erential equations or di ff erence equations, it is known that if one can display a negative definite Lyapunov function, or functionals, for ...proved boundedness of all solutions of ... See full document

... nonlinear functional dynamic equation on time scales and obtained sufficient conditions for the existence of positive ...p-Laplacian functional dynamic equations on ... See full document

... Michaelis-Menten functional response on time scales is ...to time scales. Second, we obtain the uniformly ultimate boundedness of solutions of this ... See full document

... of time scales, which play an important role in establishing the existence of solutions for ε-equivalent impulsive func- tional dynamic equations with such a ‘sight ...on time ... See full document

... differential equations and finite difference equations have been studied extensively, for example, see 1–4 and references ...on time scales, especially for p-Laplacian functional ... See full document

... on time scales [–] since the theory of dynamic equations on time scales has been a new important mathematical branch (see, for example, [– ...p-Laplacian functional ... See full document

... differential equations and finite difference equations have been studied extensively, for example see 1–4 and references ...on time scales, especially for p-Laplacian functional ... See full document

... S.enel, Oscillation theorems for the second order damped nonlinear dynamic equation on time scales, Contemp. Zhang, Oscillation of second-order half-linear delay dynamic equations with d[r] ... See full document

... differential equations, while others have studied the problem for difference equations, while still others have considered the problem for dynamic equations on a time scale ...of ... See full document

... The rest of the paper is organized as follows. In the next section, we present some basic definitions and results concerning the calculus on time scales. In Section III, we give several useful lemmas. In ... See full document

... is equivalent to the boundedness of all its solutions. DaCunha in [] defined the con- cepts of uniform stability and uniform exponential stability. These two concepts in- volve the boundedness of the ... See full document

... On time scales, one area lacking of development is the method of finding solutions on partial dynamic ...partial dynamic equations on arbitrage time ...partial dynamic ... See full document

... of time scales was first introduced by Hilger [] in  in order to study differ- ences between discrete and continuous ...The time scale calculus offers great help on unifying discrete and continuous ... See full document

... Remark 3 . We note that the oscillation criteria given in this article are new for the corresponding difference equations and some of these results are new for the correspond- ing differential and/or delay ... See full document

... the time scale analogue of well known partial dynamic equations see [1, 6, 10, ...partial dynamic equation on time ...of time scales and its ...to time ... See full document

... on time scales T unbounded from above and for which the forward jump operator has a certain explicit form given by s(t) = at + b, where a ≥ 1, b ≥ 0 are ...to time scales T that are different ... See full document

... of dynamic equations on time scales, which has recently received a lot of attention, was introduced by Hilger in his ...of time scale, that is, measure chain, by Bohner and Peterson ... See full document

... and dynamic inequal- ities on time scales ...differential equations, and it is necessary to establish new Gronwall- Bellman type inequalities so as to fulfill corresponding ... See full document

... Existence results for system (1.2) were obtained in [5] with f is a continuous function. In the particular case where n = 1, existence results for first-order ∇-dynamic equation on time scales were ... See full document

... [22] Zhang, J., Fan, M. and Zhu, H. (2009) Existence and Roughness of Exponential Di- chotomies of Linear Dynamic Equations on Time Scales. Computers & Mathemat- ics with Applications , ... See full document