Asymptotic stability and instability with respect to part of variables for solutions to impulsive systems

Ignat’ev, A. O.

doi:10.1007/s11202-008-0009-9

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Introduction and Some Historical Review1

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2010

2023

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Cited by 3 publications

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“…Certain of the relevant results are generalized in monograph [4] using piecewise differentiable auxiliary functions. The works [5,6] show the universality of the direct Lyapunov method in this class of auxiliary functions. In [7], stability conditions for solutions of a nonlinear system with impulse action were obtained based on two auxiliary functions.…”

Section: Introduction and Some Historical Reviewmentioning

confidence: 96%

Existence Results for Systems of Nonlinear Second-Order and Impulsive Differential Equations with Periodic Boundary

Moumen,

Benaissa Cherif,

Ferhat

et al. 2023

Mathematics

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A class for systems of nonlinear second-order differential equations with periodic impulse action are considered. An urgent problem for this class of differential equations is the problem of the quantitative study (existence) in the case when the phase space of the equation is, in the general case, some Banach space. In this work, sufficient conditions for the existence of solutions for a system with parameters are obtained. The results are obtained by using fixed point theorems for operators on a cone. Our approach is based on Schaefer’s fixed point theorem more precisely. In addition, the existence of positive solutions is also investigated.

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