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Volumn 17, Issue 2, 2011, Pages 235-254

Cauchy and Green matrices type and stability in alternately advanced and delayed differential systems

Author keywords

Cauchy and Green matrices; Gronwall's inequality; Hybrid equations; Piecewise constant arguments; Stability of solutions

Indexed keywords


EID: 79952931948     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236198.2010.549003     Document Type: Article
Times cited : (40)

References (34)
  • 1
    • 0001304919 scopus 로고
    • Oscillatory and periodic solutions of delay differential equations with piecewise constant argument
    • A.R. Aftabizadeh, J. Wiener, and J.M. Xu, Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. Amer. Math. Soc. 99 (1987), pp. 673-679.
    • (1987) Proc. Amer. Math. Soc. , vol.99 , pp. 673-679
    • Aftabizadeh, A.R.1    Wiener, J.2    Xu, J.M.3
  • 3
    • 33751002985 scopus 로고    scopus 로고
    • Integral manifolds of differential equations with 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), pp. 367-383.
    • (2007) Nonlinear Anal. TMA , vol.66 , pp. 367-383
    • Akhmet, M.U.1
  • 4
    • 36749034215 scopus 로고    scopus 로고
    • Stability of differential equations with piecewise constant arguments of generalized type
    • M.U. Akhmet, Stability of differential equations with piecewise constant arguments of generalized type, Nonlinear Anal. TMA 68 (2008), pp. 794-803.
    • (2008) Nonlinear Anal. TMA , vol.68 , pp. 794-803
    • Akhmet, M.U.1
  • 5
    • 33846029504 scopus 로고    scopus 로고
    • An anticipatory extension of Malthusian model, in CASYS 2005-Seventh International Conference
    • D.M. Dubois, ed., The American Institute of Physics, Liege, Belgium
    • M.U. Akhmet, Höktem, S.W. Pickl, and G.W. Weber, An anticipatory extension of Malthusian model, in CASYS 2005-Seventh International Conference, D.M. Dubois, ed., AIP Conference Proceedings, vol. 839, The American Institute of Physics, Liege, Belgium, 2006, pp. 260-264.
    • (2006) AIP Conference Proceedings , vol.839 , pp. 260-264
    • Akhmet, M.U.1    Höktem Pickl, S.W.2    Weber, G.W.3
  • 6
    • 0008359440 scopus 로고    scopus 로고
    • Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences
    • A. Alonso, J. Hong, and R. Obaya, Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences, Appl. Math. Lett. 13 (2000), pp. 131-137.
    • (2000) Appl. Math. Lett. , vol.13 , pp. 131-137
    • Alonso, A.1    Hong, J.2    Obaya, R.3
  • 8
    • 0000153927 scopus 로고
    • Models of vertically transmitted diseases with sequentialcontinuous dynamics
    • in, V. Lakshmikantham, ed., Academic Press, New York
    • S. Busenberg and K.L. Cooke, Models of vertically transmitted diseases with sequentialcontinuous dynamics, in Nonlinear Phenomena in Mathematical Sciences, V. Lakshmikantham, ed., Academic Press, New York, 1982, pp. 179-187.
    • (1982) Nonlinear Phenomena in Mathematical Sciences , pp. 179-187
    • Busenberg, S.1    Cooke, K.L.2
  • 9
    • 1542406442 scopus 로고    scopus 로고
    • Green's function and comparison principles for first order differential equations with piecewise constant arguments
    • A. Cabada, J.B. Ferreiro, and J.J. Nieto, Green's function and comparison principles for first order differential equations with piecewise constant arguments, J. Math. Anal. Appl. 291 (2004), pp. 690-697.
    • (2004) J. Math. Anal. Appl. , vol.291 , pp. 690-697
    • Cabada, A.1    Ferreiro, J.B.2    Nieto, J.J.3
  • 10
    • 77956946076 scopus 로고    scopus 로고
    • Periodic solutions of differential equations with a general piecewise constant argument and applications
    • K.S. Chiu and M. Pinto, Periodic solutions of differential equations with a general piecewise constant argument and applications, Electron. J. Qual. Theory Diff. Equ. 46 (2010), 19 pp.
    • (2010) Electron. J. Qual. Theory Diff. Equ. , vol.46 , pp. 19
    • Chiu, K.S.1    Pinto, M.2
  • 11
    • 84968468793 scopus 로고
    • An equation alternately of retarded and advanced type
    • K.L. Cooke and J. Wiener, An equation alternately of retarded and advanced type, Proc. Amer. Math. Soc. 99 (1987), pp. 726-732.
    • (1987) Proc. Amer. Math. Soc. , vol.99 , pp. 726-732
    • Cooke, K.L.1    Wiener, J.2
  • 12
    • 38249022581 scopus 로고
    • Oscillations in systems of differential equations with piecewise constant delays
    • K.L. Cooke and J. Wiener, Oscillations in systems of differential equations with piecewise constant delays, J. Math. Anal. Appl. 137 (1989), pp. 221-239.
    • (1989) J. Math. Anal. Appl. , vol.137 , pp. 221-239
    • Cooke, K.L.1    Wiener, J.2
  • 14
    • 79952981128 scopus 로고    scopus 로고
    • Source-sink impulsive bioeconomic models. Seasonal closures with fixed length
    • To appear
    • F. Cordova, E. Gonzalez-Olivares, and M. Pinto, Source-sink impulsive bioeconomic models. Seasonal closures with fixed length, J. Difference Eqs Appl. (To appear).
    • J. Difference Eqs Appl.
    • Cordova, F.1    Gonzalez-Olivares, E.2    Pinto, M.3
  • 17
    • 84972539491 scopus 로고
    • On a logistic equation with piecewise constant arguments
    • K. Gopalsamy, M.R.S. Kulenović, and G. Ladas, On a logistic equation with piecewise constant arguments, Diff. Integr. Equ. 4 (1991), pp. 215-223.
    • (1991) Diff. Integr. Equ. , vol.4 , pp. 215-223
    • Gopalsamy, K.1    Kulenović, M.R.S.2    Ladas, G.3
  • 20
    • 84968519032 scopus 로고
    • Variation of parameters formula for the equation of Cooke and Wiener
    • K.N. Jayasree and S.G. Deo, Variation of parameters formula for the equation of Cooke and Wiener, Proc. Amer. Math. Soc. 112 (1991), pp. 75-90.
    • (1991) Proc. Amer. Math. Soc. , vol.112 , pp. 75-90
    • Jayasree, K.N.1    Deo, S.G.2
  • 21
    • 0037098574 scopus 로고    scopus 로고
    • Persistence, contractivity and global stability in logistics equations with piecewise constant delays
    • Y. Muroya, Persistence, contractivity and global stability in logistics equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002), pp. 602-635.
    • (2002) J. Math. Anal. Appl. , vol.270 , pp. 602-635
    • Muroya, Y.1
  • 22
    • 0000502499 scopus 로고
    • On certain problems in the theory of differential equations with deviating arguments
    • A.D. Myshkis, On certain problems in the theory of differential equations with deviating arguments, Uspekhi Mat. Nauk 32 (1977), pp. 173-202.
    • (1977) Uspekhi Mat. Nauk , vol.32 , pp. 173-202
    • Myshkis, A.D.1
  • 23
    • 68849121933 scopus 로고    scopus 로고
    • Asymptotics for solutions of periodic difference systems
    • A. Omon and M. Pinto, Asymptotics for solutions of periodic difference systems, J. Difference Eqs Appl. 15(5) (2009), pp. 461-472.
    • (2009) J. Difference Eqs Appl. , vol.15 , Issue.5 , pp. 461-472
    • Omon, A.1    Pinto, M.2
  • 24
    • 0031274006 scopus 로고    scopus 로고
    • Linearization near the integral manifold for a system of differential equations with piecewise constant argument
    • G. Papaschinopoulos, Linearization near the integral manifold for a system of differential equations with piecewise constant argument, J. Math. Anal. Appl. 215 (1997), pp. 317-333.
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 317-333
    • Papaschinopoulos, G.1
  • 25
    • 63449115192 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonlinear and quasilinear differential equations with piecewise constant argument
    • M. Pinto, Asymptotic equivalence of nonlinear and quasilinear differential equations with piecewise constant argument, Math. Comp. Model. 49 (2009), pp. 1750-1758.
    • (2009) Math. Comp. Model. , vol.49 , pp. 1750-1758
    • Pinto, M.1
  • 28
    • 0011867164 scopus 로고    scopus 로고
    • Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence
    • G. Seifert, Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence, J. Differential Equations 164 (2000), pp. 451-458.
    • (2000) J. Differential Equations , vol.164 , pp. 451-458
    • Seifert, G.1
  • 29
    • 0042772392 scopus 로고
    • Differential equations with piecewise constant delays
    • in, V. Lakshminkantham, ed., Marcel Dekker, New York
    • J. Wiener, Differential equations with piecewise constant delays, in Trends in the Theory and Practice of Nonlinear Differential Equations, V. Lakshminkantham, ed., Marcel Dekker, New York, 1983, pp. 547-580.
    • (1983) Trends in the Theory and Practice of Nonlinear Differential Equations , pp. 547-580
    • Wiener, J.1
  • 31
    • 0033212658 scopus 로고    scopus 로고
    • Excitability of a second-order delay differential equations
    • J. Wiener and V. Lakshmikantham, Excitability of a second-order delay differential equations, Nonlinear Anal. 38 (1999), pp. 1-11.
    • (1999) Nonlinear Anal. , vol.38 , pp. 1-11
    • Wiener, J.1    Lakshmikantham, V.2
  • 32
    • 34248532288 scopus 로고    scopus 로고
    • Existence of almost periodic solutions for forced perturbed systems with piecewise constant arguments
    • Y.H. Xia, Z. Huang, and M. Han, Existence of almost periodic solutions for forced perturbed systems with piecewise constant arguments, J. Math. Anal. Appl. 333 (2007), pp. 798-816.
    • (2007) J. Math. Anal. Appl. , vol.333 , pp. 798-816
    • Xia, Y.H.1    Huang, Z.2    Han, M.3
  • 33
    • 32344446707 scopus 로고    scopus 로고
    • Green's function for second order differential equations with piecewise constant arguments
    • P. Yang, Y. Liu, and W. Ge, Green's function for second order differential equations with piecewise constant arguments, Nonlinear Anal. 64 (2006), pp. 1812-1830.
    • (2006) Nonlinear Anal. , vol.64 , pp. 1812-1830
    • Yang, P.1    Liu, Y.2    Ge, W.3
  • 34
    • 0036497509 scopus 로고    scopus 로고
    • The existence of almost periodic solutions of retarded differential equations with piecewise constant argument
    • R. Yuan, The existence of almost periodic solutions of retarded differential equations with piecewise constant argument, Nonlinear Anal. 48 (2002), pp. 1013-1032.
    • (2002) Nonlinear Anal. , vol.48 , pp. 1013-1032
    • Yuan, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.