[PDF] Top 20 WKB Estimates for Linear Dynamic Systems on Time Scales

... WKB method 1, 2 is a powerful method of the description of behavior of solutions of 1.1 by using asymptotic expansions. It was developed by Carlini 1817, Liouville, Green 1837 and became very useful in the ... See full document

... dynamical systems have a number of significant differences mainly due to the topological fact that in one case the time scale T R, real numbers, and the corresponding trajectories are connected while in ... See full document

... of dynamic equation on time scales is an area of mathematics that has recently received a lot of attention (see [1] [2] ...for dynamic equation on time ...general time ... See full document

... A further possible complication in dynamic equations (resp. a system of dynamic equa- tions) - the graininess of the time scale T - was discussed in []. Moreover, it is obvious that the bigger the ... See full document

... However, in general case, they have not been proven yet. Note that similar observations as in the next lemma can be done without difficulties when the integrals are taken over finite intervals, and also when the integrand ... See full document

... medical systems involve variables that have nonnegative sign, ...Such systems are referred to as positive ...positive systems theory is given in the monographs ... See full document

... the dynamic integral inequalities on time scales which usually can be used as handy tools to study the qualitative theory of dynamic integral equations and dynamic equations on ... See full document

... differential systems represent a natural framework for mathematical modelling of several processes in the applied sciences ...on time scales were stud- ied in ...for linear impulsive ... See full document

... for dynamic equations on time scales, which generalize the corresponding results on differential and difference ...Hamiltonian systems can be obtained by Lyapunov-type inequalities and Flo- ... See full document

... The problem of controllability to a given convex target set of a linear time-varying control system on time scales is studied. Necessary and sufficient conditions of controllability with ... See full document

... for linear dynamic equa- tions on time scales by using the unified time scale quadratic Lyapunov ...a linear time-varying system with nonlinear perturbation on time ... See full document

... of dynamic equations on time scales has been paid high attention by a lot of mathematicians [1, 3, 4, 11–13, 17, 18, 23, 26, 27, 31, ...of dynamic equations on time scales has ... See full document

... Hood (1986a) used this method to model coronal systems by including line- tying effects. These effects were analysed in greater depth by Hood, Van der Linden and Coossens (1988) who took the stability equations ... See full document

... A time scale T is an arbitrary nonempty closed subset of the real numbers R ...the time scale under consideration is not bounded above, i.e., it is a time scale interval of the form [t 0 , ∞ ) T ... See full document

... Similar results have been found starting from atypical states in the highest energy range, E ∼ 1.66, where the temperature is negative. By randomly placing vortices with an increased probability to project on the k = 2 ... 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

... 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

... A time scale T is an arbitrary nonempty closed subset of real numbers. The calculus of time scales was initiated by Stefan Hilger in his Ph.D. thesis [9] in order to create a theory that can unify ... See full document

... Zhou, “Lyapunov inequality for linear Hamiltonian systems on time scales,” Journal of Mathematical Analysis and Applications, vol.. Kaymakçalan, “Lyapunov inequalities for discrete line[r] ... See full document

... functional dynamic equation on time ...to linear and nonlinear Volterra integro-dynamic equations on time scales by displaying suitable Lyapunov ... See full document