Lyapunov-type inequalities for nonlinear impulsive systems with applications

Kayar, Zeynep
Zafer, Agacik
We obtain new Lyapunov-type inequalities for systems of nonlinear impulsive differential equations, special cases of which include the impulsive Emden-Fowler equations and half-linear equations. By applying these inequalities, sufficient conditions are derived for the disconjugacy of solutions and the boundedness of weakly oscillatory solutions.
Electronic Journal of Qualitative Theory of Differential Equations


Akhmet, Marat (2009-10-01)
At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.
Lyapunov type inequalities and their applications for linear and nonlinear systems under impulse effect
Kayar, Zeynep; Ağacık, Zafer; Department of Mathematics (2014)
In this thesis, Lyapunov type inequalities and their applications for impulsive systems of linear/nonlinear differential equations are studied. Since systems under impulse effect are one of the fundamental problems in most branches of applied mathematics, science and technology, investigation of their theory has developed rapidly in the last three decades. In addition, Lyapunov type inequalities have become a popular research area in recent years due to the fact that they provide not only better understandi...
Asymptotic integration of impulsive differential equations
Doğru Akgöl, Sibel; Ağacık, Zafer; Özbekler, Abdullah; Department of Mathematics (2017)
The main objective of this thesis is to investigate asymptotic properties of the solutions of differential equations under impulse effect, and in this way to fulfill the gap in the literature about asymptotic integration of impulsive differential equations. In this process our main instruments are fixed point theorems; lemmas on compactness; principal and nonprincipal solutions of impulsive differential equations and Cauchy function for impulsive differential equations. The thesis consists of five chapters....
New classes of differential equations and bifurcation of discontinuous cycles
Turan, Mehmet; Akhmet, Marat; Department of Mathematics (2009)
In this thesis, we introduce two new classes of differential equations, which essentially extend, in several directions, impulsive differential equations and equations on time scales. Basics of the theory for quasilinear systems are discussed, and particular results are obtained so that further investigations of the theory are guaranteed. Applications of the newly-introduced systems are shown through a center manifold theorem, and further, Hopf bifurcation Theorem is proved for a three-dimensional discontin...
Studies on the perturbation problems in quantum mechanics
Koca, Burcu; Taşeli, Hasan; Department of Mathematics (2004)
In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schrodinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.
Citation Formats
Z. Kayar and A. Zafer, “Lyapunov-type inequalities for nonlinear impulsive systems with applications,” Electronic Journal of Qualitative Theory of Differential Equations, pp. 1–13, 2016, Accessed: 00, 2020. [Online]. Available: