Dynamic Systems and Applications 12 (2003) 45-65 IMPROPER INTEGRALS ON TIME SCALES
نویسنده
چکیده
In this paper we study improper integrals on time scales. We also give some mean value theorems for integrals on time scales, which are used in the proof of an analogue of the classical Dirichlet–Abel test for improper integrals. AMS (MOS) Subject Classification. 39A10.
منابع مشابه
First order linear fuzzy dynamic equations on time scales
In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.
متن کاملDynamic Systems and Applications 12(1-2), 2003, 131-148 ASYMPTOTIC BEHAVIOR OF NATURAL GROWTH ON TIME SCALES
The asymptotic behavior of x = px is explored, with specific reference given to how the graininess of the time scale affects stability. In addition we prove a Perron type theorem for dynamic equations on time scales. The theorem gives sufficient conditions for exponential asymptotic stability of a critical point of an almost linear dynamic equation. Application to the dynamic logistic equation ...
متن کاملGeneralized Delay Integral Inequalities In Two Independent Variables On Time Scales
Abstract: In this paper, we discuss some new Gronwall-Bellman type delay integral inequalities in two independent variables on time scales, which contain arbitrary nonlinear items on unknown functions outside the integrals as well as inside the integrals. The inequalities established have different forms compared with the existing GronwallBellman type inequalities so far in the literature. As a...
متن کاملDynamic Systems and Applications 12 (2003) 23-43 EXPONENTIAL FUNCTIONS ON TIME SCALES: THEIR ASYMPTOTIC BEHAVIOR AND CALCULATION
We consider certain classes of “exponential functions” on time scales, which are defined via dynamic equations and generalize the ordinary exponential function. In this paper we are interested first in the asymptotic behavior of these functions (say compared with the ordinary exponential) and second, how to efficiently calculate matrix analogues of these functions. For the latter question we di...
متن کاملVolterra Integral Equations Governed by Highly Oscillatory Functions on Time Scales
It is well known that there are many analogies between the theories of difference equations and differential equations. The concept of time scales unifies these two situations but gives also solutions for problems on discrete sets with non-uniform step size or combinations of real and discrete intervals and many others. On the other hand, as it was seen in literature (beginning with [2]), the s...
متن کامل