... perturbation results for semi-linear dynamic equations on measure chains, New
Progress in DifferenceEquations(B.Aulbach,S.Elaydi,andG.Ladas,eds.),CRCPress,
Boca Raton, 2004.
[20] C. P
¨
otzsche and S. ... T-interval, and satis-
fies the initial condition ϕ(τ;τ,ξ, p) = ξ for τ ∈ I, ξ ∈ ᐄ,andp ∈ ᏼ.Asmentionedin
the introduction, invariant fiber bundles are generalizations...
... 2.7.
The converse follows trivially and the proof is complete.
10 Advances in Difference Equations
20 M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications,
Birkh
¨
auser, ... By the Contraction Mapping Principal, there exists a unique
solution of 3.1 and the proof is complete.
2 Advances in Difference Equations
In 12, the a...
... equation (1.1), one can replace condition (1.18) by the necessary and sufficient
condition of exponential stability of an exponential function on a time scale given in [12].
Example 1.9. Consider ... stability of dynamic equations on time scales by using calculus
on time scales [3, 4] and integral representations of solutions via asymptotic solutions [8].
A function f :
∈...
... Δ-integral
conditions for second-order dynamic equations on time scales at resonance. Advances in Difference Equations 2011
2011:42.
Submit your manuscript to a
journal and benefi t from:
7 Convenient online ... 7 of 18
RESEARC H Open Access
Solvability of boundary value problems with
Riemann-Stieltjes Δ-integral conditions for
second-order dynamic equations on time sc...
... Peterson, Dynamic Equations on Time Scales: An Introdution with Applications,
Birkh
¨
auser, Boston, Mass, USA, 2001.
23 M. Bohner and A. Peterson, Dynamic Equations on Time Scales,Birkh
¨
auser, ... Perera, and D. R. Vivero, “Multiple positive solutions in the sense
of distributions of singular BVPs on time scales and an application to Emden-Fowler equation...
... (1.1)isstudiedin[6]with
T
=
Z and p ≡ 0, and
in [5] in the case when
T
=
Z with variable p. Much of the organization of and moti-
vation for this paper arise from [5, 6].Formoreondelaydynamicequations,see ,for
Hindawi ... stability of a linear nonautonomous delay difference equa-
tion,JournalofDifference Equations and Applications 1 (1995), no. 2, 151–161.
[6] S. Hilger, Anal...
... and A. Peterson, Advances in Dynamic Equations on Time Scales,Birkh
¨
auser, Boston, Mass,
USA, 2003.
5 M. Bohner and S. H. Saker, “Oscillation of second order nonlinear dynamic equations on ... Advances in Difference Equations
9 M. Bohner, B. Karpuz, and
¨
O.
¨
Ocalan, “Iterated oscillation criteria for delay dynamic equations of first
order,” Adva...
... equations, ” International Journal
of Difference Equations, vol. 1, no. 2, pp. 181–193, 2006.
7 P. E. Kloeden and A. Zmorzynska, “Lyapunov functions for linear nonautonomous dynamical
equations on ... ∈ .
The purpose of this paper is to answer the question whether results of stability for
1.1 and 1.2 can be extended and unified for the implicit dynamic equations...
... semi-position
condition.
In this article, we are concerned with the existence of positive solutions for the following
PBVPs of impulsive dynamic equations on time scales with semi-position condition
x
△
(t) ... attention on the boundary value problems of impulsive
dynamic equations on time scales [22–36]. However, to the best of our knowle...
... of
equations of 1.1. However, there are few papers to discuss the existence of nonoscillatory
solutions for neutral delay dynamic equations on time scales.
Since we are interested in the nonoscillatory ... linear equations on a time scale,” Journal of Difference
Equations and Applications, vol. 8, no. 11, pp. 1061–1071, 2002.
6 S. H. Saker, “Oscillation criteria...