Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations

Zafer, Ağacık
New oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the form


Forced oscillation of super-half-linear impulsive differential equations
Oezbekler, A.; Zafer, Ağacık (Elsevier BV, 2007-09-01)
By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered.
Asymptotic behavior of linear impulsive integro-differential equations
Akhmet, Marat; YILMAZ, Oğuz (Elsevier BV, 2008-08-01)
Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall-Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results.
Second-order oscillation of forced functional differential equations with oscillatory potentials
Guvenilir, A. F.; Zafer, Ağacık (Elsevier BV, 2006-05-01)
New oscillation criteria are established for second-order differential equations containing both delay and advanced arguments of the form,
On periodic solutions of differential equations with piecewise constant argument
Akhmet, Marat (Elsevier BV, 2008-10-01)
The periodic quasilinear system of differential equations with small parameter and piecewise constant argument of generalized type [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA, 66 (2007) 367-383, M.U. Akhmet, On the reduction principle for differential equations with piecewise argument of generalized type, J. Math. Anal. Appl. 336 (2007) 646-663] is addressed. We consider the critical case, when associated linear homogen...
Dynamic programming for a Markov-switching jump-diffusion
Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01)
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
Citation Formats
A. ÖZBEKLER and A. Zafer, “Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 933–940, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51170.