Sturmian comparison theory for linear and half-linear impulsive differential equations

2005-11-30
Ozbekler, A.
Zafer, Ağacık
In this paper, we investigate Sturmian comparison theory for second-order half-linear differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly change the behavior of solutions in comparison. Several oscillation criteria are also derived to illustrate the results.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Suggestions

Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Picone's formula for linear non-selfadjoint impulsive differential equations
Ozbekler, A.; Zafer, Ağacık (Elsevier BV, 2006-07-15)
In this paper, we derive a Picone type formula for second-order linear non-selfadjoint impulsive differential equations having fixed moments of impulse actions, and obtain a Wirtinger type inequality, a Leighton type comparison theorem, and a Sturm-Picone comparison theorem for such equations. Moreover, several oscillation criteria are also derived as applications. (c) 2005 Elsevier Inc. All rights reserved.
Integral manifolds of differential equations with piecewise constant argument of generalized type
Akhmet, Marat (Elsevier BV, 2007-01-15)
In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG). The existence of global integral manifolds of the quasilinear EPCAG is established when the associated linear homogeneous system has an exponential dichotomy. The smoothness of the manifolds is investigated. The existence of bounded and periodic solutions is considered. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Ap...
Matrix measure approach to Lyapunov-type inequalities for linear Hamiltonian systems with impulse effect
Kayar, Zeynep; Zafer, Ağacık (Elsevier BV, 2016-08-01)
We present new Lyapunov-type inequalities for Hamiltonian systems, consisting of 2n-first-order linear impulsive differential equations, by making use of matrix measure approach. The matrix measure estimates of fundamental matrices of linear impulsive systems are crucial in obtaining sharp inequalities. To illustrate usefulness of the inequalities we have derived new disconjugacy criteria for Hamiltonian systems under impulse effect and obtained new lower bound estimates for eigenvalues of impulsive eigenva...
Asymptotic behavior of Markov semigroups on preduals of von Neumann algebras
Ernel'yanov, EY; Wolff, MPH (Elsevier BV, 2006-02-15)
We develop a new approach for investigation of asymptotic behavior of Markov semigroup on preduals of von Neumann algebras. With using of our technique we establish several results about mean ergodicity, statistical stability, and constrictiviness of Markov semigroups. (c) 2005 Elsevier Inc. All rights reserved.
Citation Formats
A. Ozbekler and A. Zafer, “Sturmian comparison theory for linear and half-linear impulsive differential equations,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 0–0, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51546.