[PDF] Top 20 Variational approach to second-order impulsive dynamic equations on time scales

... of impulsive dynamic equations arise in biology (biological phenomena involving thresholds), medicine (bursting rhythm models), pharmacokinetics, mechanics, engineering, chaos ...of impulsive ... See full document

... The time scale calculus has tremendous potential for applications in mathematical models of real processes, for example, in physics, chemical technology, population dynamics, biotechnology and economics, neural ... 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

... of impulsive differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equa- tions without impulse ...such ... See full document

... of impulsive differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equations without impulse ...such ... See full document

... This work is generalized as follows: Section  contains a brief summary of the theory of fuzzy sets and calculus of time scales. Section  deals with the fuzzy calculus on time scales. Then in ... See full document

... advanced dynamic equation on time scales, such as the h- difference equation (h > 0), and it is also called a finite difference equation, ...differential equations on time ... See full document

... the second-order nonlinear delay dynamic equations on time ...the second-order nonlinear delay differential equation and the second-order nonlinear delay ... See full document

... interesting time scales exist, and they give rise to plenty of applications, among them the study of population dynamic models which are discrete in season and may follow a difference scheme with ... See full document

... delay dynamic equation (.) on time scales, where  < α ≤  is the quotient of odd positive integers and established some suf- ficient conditions for oscillations when ...quasi-linear ... See full document

... The paper is organized as follows. In the next section, by developing a Riccati transformation technique some sufficient conditions for oscillation of all solutions of 1.1 on time scales are established. In ... See full document

... Neutral equations find numerous applications in natural science and technology. For instance, they are frequently used for the study of distributed networks containing lossless transmission lines. So, we try to ... See full document

... of τ(t) ≤ t, assumption τ(δ(t)) < t is already satisfied when δ(t) < t and the proofs do not change. Assumption τ(t) < t implies the immediate result τ(δ(t)) < δ(t). Therefore, we conclude the following which ... See full document

... of dynamic equations on time scales, we refer the reader to [1–23] and the references cited ...of dynamic equations with damp- ing attracted significant attention of researchers ... See full document

... of second-order damped dynamic equations on time scale which attempts to harmonize the oscillation theory for continuousness and discreteness, to include them in one comprehensive ... See full document

... This paper is organized as follows. In Section 2, we present some preliminary results concerning the time scales calculus and Sobolev’s spaces on time scales. In Section 3, we construct a ... See full document

... We assume that γ > 0 is a quotient of odd positive integers, r and p are positive, real- valued rd-continuous functions defined on T, τ : T → R is strictly increasing, and T : τT ⊂ T is a time scale, τ t ≤ t ... See full document

... of dynamic equations on time scales has been a new important mathematical branch [–] since it was initiated by Hilger ...same time, the boundary value problems of impulsive ... See full document

... various equations on time scales, and we refer the reader to Bohner and Saker [5], Erbe [6], Erbe et ...delay dynamic equations on time scales ... See full document

... m   t p t       t [3] L. H. Erbe, “Oscillation Criteria for Second Order Linear Equations on Atime Scale,” Canadian Applied Mathe- matics Quarterly, Vol. 9, No. 4, 2001, pp. 345-375. [4] A. ... See full document