메뉴 건너뛰기




Volumn 64, Issue 1, 2006, Pages 137-151

On stability of linear time-varying second-order differential equations

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING;

EID: 33645931326     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0033-569X-06-00995-X     Document Type: Article
Times cited : (35)

References (19)
  • 1
    • 0001034477 scopus 로고
    • On the asymptotic stability of oscillators with unbounded damping
    • MR0466789 (57:6665)
    • Z. Artstein and E.F. Infante, On the asymptotic stability of oscillators with unbounded damping. Quart. Appl. Math. 34 (1976/77), no. 2, 195-199. MR0466789 (57:6665)
    • (1976) Quart. Appl. Math. , vol.34 , Issue.2 , pp. 195-199
    • Artstein, Z.1    Infante, E.F.2
  • 2
    • 0001274382 scopus 로고
    • Systèmes d'équations différentielles d'oscillations nonlinéaires
    • Bucharest IV MR0111896 (22:2754b)
    • I. Barbǎlat, Systèmes d'équations différentielles d'oscillations nonlinéaires, Revue de Mathématiques Pures et Appliquées, Bucharest IV (1959), 267-270. MR0111896 (22:2754b)
    • (1959) Revue De Mathématiques Pures Et Appliquées , pp. 267-270
    • Barbǎlat, I.1
  • 3
    • 0014612955 scopus 로고
    • Slowly varying system ẋ= A(t)x
    • MR0276562 (43:2306)
    • C.E. Desoer, Slowly varying system ẋ= A(t)x. IEEE Trans. Automatic Control 14 (1969), 780-781. MR0276562 (43:2306)
    • (1969) IEEE Trans. Automatic Control , vol.14 , pp. 780-781
    • Desoer, C.E.1
  • 4
    • 60349098073 scopus 로고    scopus 로고
    • Lyapunov and other spectra: A survey
    • Collected lectures on the preservation of stability under discretization (Fort Collins, CO, 2001)SIAM, Philadelphia, PA MR2026670
    • L. Dieci and E. Van Vleck, Lyapunov and other spectra: a survey. Collected lectures on the preservation of stability under discretization (Fort Collins, CO, 2001), 197-218, SIAM, Philadelphia, PA, 2002. MR2026670
    • (2002) , pp. 197-218
    • Dieci, L.1    Van Vleck, E.2
  • 5
    • 21344431566 scopus 로고    scopus 로고
    • Integral conditions on the asymptotic stability for the damped linear oscillator with small damping
    • MR1317039 (96d:34062)
    • L. Hatvani, Integral conditions on the asymptotic stability for the damped linear oscillator with small damping. Proc. Amer. Math. Soc. 124 (1996), 415-422. MR1317039 (96d:34062)
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 415-422
    • Hatvani, L.1
  • 6
    • 0001561980 scopus 로고
    • A necessary and sufficient condition for the asymptotic stability of the damped oscillator
    • L. Hatvani, T. Krisztin, and V. Totik, A necessary and sufficient condition for the asymptotic stability of the damped oscillator. J. Differential Equations 119 (1995), 209-223.
    • (1995) J. Differential Equations , vol.119 , pp. 209-223
    • Hatvani, L.1    Krisztin, T.2    Totik, V.3
  • 7
    • 84968512344 scopus 로고
    • Singular perturbations on the infinite interval
    • MR0194693 (33:2900)
    • F.C. Hoppenstaed, Singular perturbations on the infinite interval. Trans. Am. Math. Soc. 123 (1966), 521-535. MR0194693 (33:2900)
    • (1966) Trans. Am. Math. Soc. , vol.123 , pp. 521-535
    • Hoppenstaed, F.C.1
  • 8
    • 85039343573 scopus 로고    scopus 로고
    • Asymptotic stability for second-order differential equations with complex coefficients
    • MR2075424 (2005f:34141)
    • C.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients. Electron. J. Differential Equations 85 (2004), 20 pp. MR2075424 (2005f:34141)
    • (2004) Electron. J. Differential Equations , vol.85 , pp. 20
    • Hovhannisyan, G.R.1
  • 9
    • 0242672552 scopus 로고    scopus 로고
    • Stability of a linear oscillator with variable parameters
    • MR1476064 (98i:34076)
    • A.O. Ignatyev, Stability of a linear oscillator with variable parameters. Electron. J. Differential Equations 17 (1997), 6 pp. MR1476064 (98i:4076)
    • (1997) Electron. J. Differential Equations , vol.17 , pp. 6
    • Ignatyev, A.O.1
  • 10
    • 34250961888 scopus 로고
    • Global asymptotic stability for nonlinear systems of differential equations and applications to reactor dynamics
    • MR0119524 (22:10285)
    • J.J. Levin and J.A. Nohel, Global asymptotic stability for nonlinear systems of differential equations and applications to reactor dynamics. Arch. Rational Mech. Anal. 5 (1960), 194-211. MR0119524 (22:10285)
    • (1960) Arch. Rational Mech. Anal. , vol.5 , pp. 194-211
    • Levin, J.J.1    Nohel, J.A.2
  • 11
    • 0000282907 scopus 로고
    • Precise damping conditions for global asymptotic stability for nonlinear second order systems
    • MR1226530 (94i:34103)
    • P. Pucci and J. Serrin, Precise damping conditions for global asymptotic stability for nonlinear second order systems. Acta Math. 170 (1993), no. 2, 275-307. MR1226530 (94i:34103)
    • (1993) Acta Math. , vol.170 , Issue.2 , pp. 275-307
    • Pucci, P.1    Serrin, J.2
  • 12
    • 33646051721 scopus 로고
    • Precise damping conditions for global asymptotic stability for nonlinear second order systems. II
    • MR1297668 (95m:34088)
    • P. Pucci and J. Serrin, Precise damping conditions for global asymptotic stability for nonlinear second order systems. II. J. Differential Equations 113 (1994), no. 2, 505-534. MR1297668 (95m:34088)
    • (1994) J. Differential Equations , vol.113 , Issue.2 , pp. 505-534
    • Pucci, P.1    Serrin, J.2
  • 13
    • 21344476181 scopus 로고
    • Asymptotic stability for intermittently controlled nonlinear oscillators
    • MR1271312 (95c:34092)
    • P. Pucci and J. Serrin, Asymptotic stability for intermittently controlled nonlinear oscillators. SIAM J. Math. Anal. 25 (1994), no. 3, 815-835. MR1271312 (95c:34092)
    • (1994) SIAM J. Math. Anal. , vol.25 , Issue.3 , pp. 815-835
    • Pucci, P.1    Serrin, J.2
  • 14
    • 84915729501 scopus 로고
    • The stability of linear time-dependent control systems
    • MR0159085 (28:2303)
    • H.H. Rosenbrock, The stability of linear time-dependent control systems. J. Electronics Control 15 (1963), 73-80. MR0159085 (28:2303)
    • (1963) J. Electronics Control , vol.15 , pp. 73-80
    • Rosenbrock, H.H.1
  • 15
    • 0003728020 scopus 로고    scopus 로고
    • 2nd ed., Prentice-Hall, Englewood Cliffs, New Jersey. MR1211190 (94b:93002)
    • W.J. Rugh (1996), Linear System Theory 2nd ed., Prentice-Hall, Englewood Cliffs, New Jersey. MR1211190 (94b:93002)
    • (1996) Linear System Theory
    • Rugh, W.J.1
  • 16
    • 49349126301 scopus 로고
    • A Spectral Theory for Linear Differential Systems
    • MR0501182 (58:18604)
    • R.J. Sacker and G.R. Sell, A Spectral Theory for Linear Differential Systems. J. Differential Equations 27 (1978), 320-358. MR0501182 (58:18604)
    • (1978) J. Differential Equations , vol.27 , pp. 320-358
    • Sacker, R.J.1    Sell, G.R.2
  • 17
    • 0008511747 scopus 로고    scopus 로고
    • Dichotomy spectrum for nonautonomous differential equations
    • MR1878650 (2002j:34082)
    • S. Siegmund, Dichotomy spectrum for nonautonomous differential equations. J. Dynam. Differential Equations 14 (2002), no. 1, 243-258. MR1878650 (2002j:34082)
    • (2002) J. Dynam. Differential Equations , vol.14 , Issue.1 , pp. 243-258
    • Siegmund, S.1
  • 18
    • 84963087484 scopus 로고
    • Asymptotic stability of x″ + a(t)x′ + x = 0
    • MR0124582 (23:A1894)
    • R.A. Smith, Asymptotic stability of x″ + a(t)x′ + x = 0. Quart. J. Math. Oxford Ser. (2) 12 (1961), 123-126. MR0124582 (23:A1894)
    • (1961) Quart. J. Math. Oxford Ser. , vol.12 , Issue.2 , pp. 123-126
    • Smith, R.A.1
  • 19
    • 0001485469 scopus 로고
    • On the stability of slowly time-varying linear systems
    • MR1359034 (96k:34108)
    • V. Solo, On the stability of slowly time-varying linear systems. Math. Control Signals Systems 7 (1994), no. 4, 331-350. MR1359034 (96k:34108)
    • (1994) Math. Control Signals Systems , vol.7 , Issue.4 , pp. 331-350
    • Solo, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.