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  1. Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonl...

    Authors: Elvan Akin-Bohner and Youssef N Raffoul
    Citation: Advances in Difference Equations 2006 2006:079689
  2. We examine the conditions of asymptotic stability of second-order linear dynamic equations on time scales. To establish asymptotic stability we prove the stability estimates by using integral representations o...

    Authors: Gro Hovhannisyan
    Citation: Advances in Difference Equations 2006 2006:018157
  3. In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pai...

    Authors: Petr Stehlík
    Citation: Advances in Difference Equations 2006 2006:073860
  4. We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.

    Authors: Martin Bohner and Gusein Sh Guseinov
    Citation: Advances in Difference Equations 2006 2006:026391
  5. Starting from supersymmetric quantum mechanics and related supermodels within Schrödinger theory, we review the meaning of self-similar superpotentials which exhibit the spectrum of a geometric series. We cons...

    Authors: Nicole Garbers and Andreas Ruffing
    Citation: Advances in Difference Equations 2006 2006:072768
  6. We investigate the existence and uniqueness of solutions to a class of discrete hyperbolic systems with some nonlinear extreme conditions and initial data, in a real Hilbert space.

    Authors: Rodica Luca
    Citation: Advances in Difference Equations 2006 2006:089260
  7. We consider the stability problem for the difference system x n = Axn-1 + Bxn-k, where A, B are real matrixes and the delay k is a positive integer. In the case A = -I, the equa...

    Authors: Mikhail Kipnis and Darya Komissarova
    Citation: Advances in Difference Equations 2006 2006:031409
  8. We construct invariant foliations of the extended state space for nonautonomous semilinear dynamic equations on measure chains (time scales). These equations allow a specific parameter dependence which is the ...

    Authors: Christian Pötzsche
    Citation: Advances in Difference Equations 2006 2006:057043
  9. Difference schemes for two-point boundary value problems for systems of first-order nonlinear ordinary differential equations are considered. It was shown in former papers of the authors that starting from the...

    Authors: IP Gavrilyuk, M Hermann, MV Kutniv and VL Makarov
    Citation: Advances in Difference Equations 2006 2006:012167
  10. The aim of this paper is to discuss the oscillatory behavior of difference systems of mixed type. Several criteria for oscillations are obtained. Particular results are included in regard to scalar equations.

    Authors: JoséM Ferreira and Sandra Pinelas
    Citation: Advances in Difference Equations 2006 2006:092923
  11. We discuss the existence of oscillatory and nonoscillatory solutions for first-order impulsive dynamic equations on time scales with certain restrictions on the points of impulse. We will rely on the nonlinear...

    Authors: Mouffak Benchohra, Samira Hamani and Johnny Henderson
    Citation: Advances in Difference Equations 2006 2006:060860
  12. We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of func...

    Authors: Ravi P Agarwal, Victoria Otero–Espinar, Kanishka Perera and Dolores R Vivero
    Citation: Advances in Difference Equations 2006 2006:038121
  13. We discuss conditions for the existence of at least one positive solution to a nonlinear second-order Sturm-Liouville-type multipoint eigenvalue problem on time scales. The results extend previous work on both...

    Authors: Douglas R Anderson and Ruyun Ma
    Citation: Advances in Difference Equations 2006 2006:059572
  14. Essentially nonlinear difference equations in a Euclidean space are considered. Conditions for the existence of periodic solutions and solution estimates are derived. Our main tool is a combined usage of the r...

    Authors: MI Gil'
    Citation: Advances in Difference Equations 2006 2006:039419
  15. Linear neutral, and especially non-neutral, Volterra difference equations with infinite delay are considered and some new results on the behavior of solutions are established. The results are obtained by the u...

    Authors: Ch G Philos and IK Purnaras
    Citation: Advances in Difference Equations 2006 2006:078470
  16. We first give conditions which guarantee that every solution of a first order linear delay dynamic equation for isolated time scales vanishes at infinity. Several interesting examples are given. In the last ha...

    Authors: Douglas R Anderson, Robert J Krueger and Allan C Peterson
    Citation: Advances in Difference Equations 2006 2006:094051
  17. Nonoscillatory solutions of a nonlinear neutral type higher order difference equations are classified by means of their asymptotic behaviors. By means of the Kranoselskii's fixed point theorem, existence crite...

    Authors: Zhi-qiang Zhu, Gen-qiang Wang and Sui Sun Cheng
    Citation: Advances in Difference Equations 2006 2006:047654

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