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Dynamic Equations with Applications

  1. Research Article

    Boundedness in functional dynamic equations on time scales

    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...

    Elvan Akin-Bohner and Youssef N Raffoul

    Advances in Difference Equations 2006 2006:079689

    Published on: 28 September 2006

  2. Research Article

    Asymptotic stability for dynamic equations on time scales

    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...

    Gro Hovhannisyan

    Advances in Difference Equations 2006 2006:018157

    Published on: 27 September 2006

  3. Research Article

    On lower and upper solutions without ordering on time scales

    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...

    Petr Stehlík

    Advances in Difference Equations 2006 2006:073860

    Published on: 13 September 2006

  4. Research Article

    Multiple Lebesgue integration on time scales

    We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.

    Martin Bohner and Gusein Sh Guseinov

    Advances in Difference Equations 2006 2006:026391

    Published on: 10 September 2006

  5. Research Article

    Using supermodels in quantum optics

    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...

    Nicole Garbers and Andreas Ruffing

    Advances in Difference Equations 2006 2006:072768

    Published on: 5 September 2006

  6. Research Article

    The formulation of second-order boundary value problems on time scales

    We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on time scales. Although this topic has received extensive attention in recent years, we present som...

    Fordyce A Davidson and Bryan P Rynne

    Advances in Difference Equations 2006 2006:031430

    Published on: 13 July 2006

  7. Research Article

    Invariant foliations and stability in critical cases

    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 ...

    Christian Pötzsche

    Advances in Difference Equations 2006 2006:057043

    Published on: 9 July 2006