No abstract

No abstract

We establish the best (minimum) constant for Ulam stability of first-order linear hdifference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation with a period-two coefficient, and give several examples. In the last section we prove Ulam stability for a periodic coefficient function of arbitrary finite period. Results on the associated first-order perturbed linear equation with periodic coefficient are also included.2010 Mathematics Subject Classification. 39A10, 34N05, 39A23, 39A45.

No abstract

No abstract

The equation considered in this paper is t p (φp(x )) + g(x) = 0, where φp(x ) = |x | p−2 x with p > 1, and g(x) satisfies the signum condition xg(x) > 0 if x = 0 but is not assumed to be monotone. Our main objective is to establish a criterion on g(x) for all non-trivial solutions to be non-oscillatory. The criterion is the best possible. The method used here is the phase-plane analysis of a system equivalent to this differential equation. The asymptotic behaviour is also examined in detail for eventually positive solutions of a certain half-linear differential equation.

We establish the stability of higher-order linear nonhomogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact solution to that dynamic equation that is close to the approximate one. Some examples illustrate the applicability of the main results.2010 Mathematics Subject Classification. 34N05, 26E70, 39A10.

No abstract