New oscillation criteria are given for the second order sublinear differential equation $${\left[a\left(t\right)\psi \left(x\left(t\right)\right)x^{\text{'}}\left(t\right)\right]}^{\text{'}}+q\left(t\right)f\left(x\left(t\right)\right)=0,t\ge t_0>0,$$ where $a\in C^1\left([t_0,\infty )\right)$ is a nonnegative function, $\psi ,f\in C\left(ℝ\right)$ with $\psi \left(x\right)\ne 0$, $xf\left(x\right)/\psi \left(x\right)>0$ for $x\ne 0$, $\psi$, $f$ have continuous derivative on $ℝ\setminus \left\{0\right\}$ with ${[f\left(x\right)/\psi \left(x\right)]}^{\text{'}}\ge 0$ for $x\ne 0$ and $q\in C\left([t_0,\infty )\right)$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^{\text{'}\text{'}}\left(t\right)+q\left(t\right)x\left(t\right)=0$.

This paper is concerned with the oscillatory behavior of the damped half-linear oscillator ${\left(a\left(t\right){\phi }_p\left(x^{\text{'}}\right)\right)}^{\text{'}}+b\left(t\right){\phi }_p\left(x^{\text{'}}\right)+c\left(t\right){\phi }_p\left(x\right)=0$, where ${\phi }_p\left(x\right)={\left|x\right|}^{p-1}\mathrm{sgn}x$ for $x\in ℝ$ and $p>1$. A sufficient condition is established for oscillation of all nontrivial solutions of the damped half-linear oscillator under the integral averaging conditions. The main result can be given by using a generalized Young’s inequality and the Riccati type technique. Some examples are included to illustrate the result. Especially, an example which asserts that all nontrivial solutions are...

This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference...

Si studia l'equivalenza asintotica fra le soluzioni di un sistema lineare e quelle di una perturbazione non lineare. Vengono date condizioni sufficienti per l'esistenza di un omeomorfìsmo fra le soluzioni limitate di tali sistemi.

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.Sufficient conditions are obtained for the existence of local integral manifolds of autonomous systems of differential equations with impulses at fixed moments. In case of perturbations of the nonlinear part an estimate of the difference between the manifolds is obtained.