QUASILINEAR RETARDED DIFFERENTIAL EQUATIONS WITH FUNCTIONAL DEPENDENCE ON PIECEWISE CONSTANT ARGUMENT

被引：10

作者：

Akhmet, M. U. ^{[1
]}

机构：

[1] Middle E Tech Univ, Dept Math, TR-06531 Ankara, Turkey

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 02期

关键词：

Retarded differential equations; functional dependence on piecewise constant argument; alternate constancy of argument; periodic solutions; Bohr almost periodic solutions; exponential stability; ALMOST-PERIODIC SOLUTIONS; GENERALIZED TYPE; SUFFICIENT CONDITION; TIME-DEPENDENCE; DELAY EQUATION; STABILITY; SPECTRUM;

D O I：

10.3934/cpaa.2014.13.929

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a new class of differential equations, retarded differential equations with functional dependence on piecewise constant argument, RFDEPCA, and focus on quasilinear systems. Formulation of the initial value problem, bounded solutions, periodic and almost periodic solutions, their stability are under investigation. Illustrating examples are provided.

引用

页码：929 / 947

页数：19

共 36 条

[1] On periodic solutions of differential equations with piecewise constant argument [J].

Akhmet, M. U. ;

Buyukadali, C. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (08) :2034-2042

[2] Stability of differential equations with piecewise constant arguments of generalized type [J].

Akhmet, M. U. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (04) :794-803

[3] On the reduction principle for differential equations with piecewise constant argument of generalized type [J].

Akhmet, M. U. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (01) :646-663

[4] Integral manifolds of differential equations with piecewise constant argument of generalized type [J].

Akhmet, M. U. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (02) :367-383

[5] Method of Lyapunov functions for differential equations with piecewise constant delay [J].

Akhmet, M. U. ;

Arugaslan, D. ;

Yilmaz, E. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (16) :4554-4560

[6] Stability analysis of recurrent neural networks with piecewise constant argument of generalized type [J].

Akhmet, M. U. ;

Arugaslan, D. ;

Yilmaz, E. .

NEURAL NETWORKS, 2010, 23 (07) :805-811

[7] Differential equations with state-dependent piecewise constant argument [J].

Akhmet, M. U. ;

Buyukadali, C. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (11) :4200-4210

[8] LYAPUNOV-RAZUMIKHIN METHOD FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT [J].

Akhmet, Marat ;

Arugaslan, Duygu .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (02) :457-466

[9]

AKHMET MU, 2012, DISCONTINUITY NONLIN, V1, P337

[10]

Akhmetov MU, 1983, AKAD NAUK UKRAIN SSR, V26, P49

← 1 2 3 4 →