Oscillation of Second-Order Sublinear Impulsive Differential Equations

2011
Zafer, A.
Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type: x ''(t) + p(t)vertical bar x(tau(t))vertical bar(alpha-1)x(tau(t)) = 0, t not equal theta(k); Delta x'(t)vertical bar(t=theta k) + q(k)vertical bar x(tau(theta(k)))vertical bar(alpha-1)x(tau(theta(k))) = 0; Delta x(t)vertical bar(t=theta k) = 0, (0 < alpha < 1) by considering the cases tau(t) <= t and tau(t) = t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.
Abstract and Applied Analysis

Suggestions

Oscillation criteria for third-order nonlinear functional differential equations
AKTAŞ, MUSTAFA FAHRİ; Tiryaki, A.; Zafer, Ağacık (Elsevier BV, 2010-07-01)
In this work, we are concerned with oscillation of third-order nonlinear functional differential equations of the form
Differential equations with state-dependent piecewise constant argument
Akhmet, Marat (Elsevier BV, 2010-06-01)
A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution are obtained. Appropriate examples are constructed.
On Stability of Linear Delay Differential Equations under Perron's Condition
Diblík, J.; Zafer, A. (Hindawi Limited, 2011)
The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.
Integral criteria for oscillation of third order nonlinear differential equations
AKTAŞ, MUSTAFA FAHRİ; Tiryaki, Aydın; Zafer, Ağacık (Elsevier BV, 2009-12-15)
In this paper we are concerned with the oscillation of third order nonlinear differential equations of the form
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...
Citation Formats
A. Zafer, “Oscillation of Second-Order Sublinear Impulsive Differential Equations,” Abstract and Applied Analysis, pp. 1–11, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50986.