[PDF] Top 20 First and second order dynamic equations with impulse

... with impulse, Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations (Mississippi, 1997), ...of second order ... See full document

... of dynamic equations on time scales which goes back to its founder Hilger [1] as an area of mathematics that has received a lot of ...in order to unify the study of differential and difference ... 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 theory, and ... See full document

... For the existence and uniqueness of solutions of the equations of the form 1.6, refer to the monograph 2 . As usual, we define a proper solution of 1.6 which is said to be oscillatory if it is neither eventually ... See full document

... is studied in [32] (they assume γ is an odd positive integer) and the Riccati dynamic equation (2.5) is studied extensively in [23]. A number of oscillation criteria are also given based on the variational ... See full document

... On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales Quanxin Zhang, Xia Song, Li Gao Department of Mathematics, Binzhou University, Shandong, China[r] ... See full document

... In 1990, Hilger introduced in [7] the theory of time scales with one goal being the unified treatment of differential equations (the continuous case) and difference equations (the discrete case). A time scale ... See full document

... q-difference equations initiated at the beginning of the twentieth century [–] is a very interesting field in difference ...q-difference equations is still in the initial stages and many aspects of this ... See full document

... The aim of this paper is to use variational techniques and critical point theory to derive the existence of multiple solutions to (P); we refer the reader to [–] for a broad intro- duction to dynamic ... See full document

... criteria for the oscillation of (). Their results covered those for differential equations and offered new oscillation criteria for difference equations. Medico and Kong [] extended the work in [] by ... See full document

... Oscillation, as a kind of physical phenomena, widely exists in the natural sciences and engineering. For instance, self-excited vibration in control system, beam vibration in syn- chrotron accelerator, the complicated ... See full document

... [3] OK Famurewa, RA Ademiluyi, and DO Awoyemi. A comparative study of a class of implicit multi-derivative meth- ods for numerical solution of non-stiff and stiff first order ordinary differential ... See full document

... the second order fuzzy dynamic equations on time scales and defined a new ...first order fuzzy dynamic equations on time scales in ...to second order fuzzy ... See full document

... of equations with nonnegative neutral coefficients; see, ...for equations with nonpositive neutral coefficients, there are relatively fewer results in the literature; see [3, 4, 6, 11, 14, ... See full document

... presented that not only complement and improve those related results in the literature, but also improve some known results for a second-order delay dynamic equation without a neutral term. Further, ... See full document

... For dynamic equations on time scales with positive variable coefficients and several delays, we prove that nonoscillation is equivalent to the existence of a positive solution for the generalized ... See full document

... This paper is concerned with oscillation and asymptotic behavior of a second-order neutral delay dynamic equation on an arbitrary time scale. We obtain two theorems which guarantee that every ... See full document

... to second-order dynamic equations in ...the second order nonlinear dynamic equations on time scales can be found in 11–23, and the references cited ... See full document

... of dynamic equations on time ...about equations when no explicit sign assumptions are made with respect to the coefficient functions p, q, and ... See full document

... As we know, the fixed point theorem of cone expression and compression is extensively used to study the existence of multiple solutions of boundary value problems for second- order differential ... See full document