Ulam’s type stability of impulsive ordinary differential equations☆

We present a survey of some selected recent developments (results and methods) in the theory of Ulam's type stability In particular we provide some information on hyperstability and the fixed point methods

/pdf/on-some-recent-developments-in-ulam-s-type-stability-2ud5g7wiwd.pdf

On Some Recent Developments in Ulam's Type Stability

Hyers–Ulam stability of nonlinear differential equations with fractional integrable impulses

We study scalar advanced and delayed differential equations with piecewise constant generalized arguments, in short DEPCAG of mixed type, that is, the arguments are general step functions. It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without the argument deviations. Criteria for existence of periodic solutions of such equations are discussed. New criteria extend and improve related results reported in the literature. The efficiency of our criteria is illustrated via several numerical examples and simulations.

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second order . That is, if is an approximate solution of the equation , then there exists an exact solution of the equation near to .

/pdf/hyers-ulam-stability-of-nonhomogeneous-linear-differential-kbt1szsxw3.pdf

Yan Shen

Papers

Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order