Auto-Oscillations in Continuous Systems with Impulsive Self-Support

The surway of impulsive-continuous autonomous systems of various types is represented, especially those of in which the impulsive self-suport (ISS) generates discontinuous auto-oscillations. The main objects are: discontinuous dynamical systems, linear oscillator with one degree of freedom and ISS, scalar functional differential equations with ISS, heat conductions and vibration of the string with energy dissipation and ISS

Asymptotic equivalence of impulsive differential equations in a Banach space

By means of Schauder's fixed point theorem sufficient conditions for asymptotic equivalence of impulsive equations in a Banach space are found

On the oscillatory properties of the solutions of a class of integro-differential equations of neutral type

In the present paper the oscillatory properties of the solutions of the equation[(Lx)(t)](n)+∫ItK(t,s,x(s))ds=0are investigated where n≥1, L is an operator of the difference type, It⊂ℝ, K:DK→ℝ, DK⫅ℝ3, x:[αx,∞]→ℝ. Under natural conditions imposed on L, It and K it is proved that for n even all ultimately nonzero solutions oscillate and for n odd they either oscillate or tend to zero as t→∞

Asymptotic equivalence of impulsive differential equations in a Banach space

By means of Schauder's fixed point theorem sufficient conditions for asymptotic equivalence of impulsive equations in a Banach space are found