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Volumn 344, Issue 5, 2007, Pages 391-398

On the asymptotic behavior of solutions of certain second-order differential equations

Author keywords

Asymptotic behavior; Differential equations of second order

Indexed keywords

ASYMPTOTIC ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; LYAPUNOV FUNCTIONS;

EID: 34248525917     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2006.02.011     Document Type: Article
Times cited : (58)

References (29)
  • 1
    • 27544455866 scopus 로고    scopus 로고
    • On the stability of the Liénard equation with unsteady perturbations
    • Aleksandrov A.Y. On the stability of the Liénard equation with unsteady perturbations. Differ. Uravn. 32 5 (1996) 702-703
    • (1996) Differ. Uravn. , vol.32 , Issue.5 , pp. 702-703
    • Aleksandrov, A.Y.1
  • 2
    • 27144526715 scopus 로고    scopus 로고
    • Translation in Differential Equations, 32 (5) (1996) 712-713.
  • 5
    • 0242564039 scopus 로고
    • Boundedness, periodicity, and convergence of solutions in a retarded Liénard equation
    • Burton T.A., and Zhang B. Boundedness, periodicity, and convergence of solutions in a retarded Liénard equation. Ann. Mat. Pura Appl. 165 4 (1993) 351-368
    • (1993) Ann. Mat. Pura Appl. , vol.165 , Issue.4 , pp. 351-368
    • Burton, T.A.1    Zhang, B.2
  • 6
    • 1542782908 scopus 로고    scopus 로고
    • On the stability of the origin of a nonautonomous Liénard equation
    • Cantarelli G. On the stability of the origin of a nonautonomous Liénard equation. Boll. Un. Mat. Ital. A 10 7 (1996) 563-573
    • (1996) Boll. Un. Mat. Ital. A , vol.10 , Issue.7 , pp. 563-573
    • Cantarelli, G.1
  • 7
    • 34248522478 scopus 로고
    • The degree of structural instability of the focus in the Liénard equation
    • Cerkas L.A. The degree of structural instability of the focus in the Liénard equation. Dokl. Akad. Nauk BSSR 23 8 (1979) 681-683
    • (1979) Dokl. Akad. Nauk BSSR , vol.23 , Issue.8 , pp. 681-683
    • Cerkas, L.A.1
  • 8
    • 0042886536 scopus 로고    scopus 로고
    • On the asymptotic behavior of the solutions of some third and fourth order non-autonomous differential equations
    • Hara T. On the asymptotic behavior of the solutions of some third and fourth order non-autonomous differential equations. Publ. Res. Inst. Math. Sci. 9 (197374) 649-673
    • Publ. Res. Inst. Math. Sci. , vol.9 , pp. 649-673
    • Hara, T.1
  • 9
    • 1642500627 scopus 로고
    • On the stability of the zero solution of nonlinear second order differential equations
    • Hatvani L. On the stability of the zero solution of nonlinear second order differential equations. Acta Sci. Math. 57 (1993) 367-371
    • (1993) Acta Sci. Math. , vol.57 , pp. 367-371
    • Hatvani, L.1
  • 10
    • 34248543338 scopus 로고
    • Global asymptotic stability of a generalized Liénard equation
    • Heidel J.W. Global asymptotic stability of a generalized Liénard equation. SIAM J. App. Math. 19 3 (1970) 629-636
    • (1970) SIAM J. App. Math. , vol.19 , Issue.3 , pp. 629-636
    • Heidel, J.W.1
  • 11
    • 0010932059 scopus 로고
    • A Liapunov function for a generalized Liénard equation
    • Heidel J.W. A Liapunov function for a generalized Liénard equation. J. Math. Anal. Appl. 39 (1972) 192-197
    • (1972) J. Math. Anal. Appl. , vol.39 , pp. 192-197
    • Heidel, J.W.1
  • 12
    • 34248564493 scopus 로고    scopus 로고
    • Another elementary proof of the stability criterion of Liénard and Chipart
    • Jia L. Another elementary proof of the stability criterion of Liénard and Chipart. Quart. J. Math. 14 3 (1999) 76-79
    • (1999) Quart. J. Math. , vol.14 , Issue.3 , pp. 76-79
    • Jia, L.1
  • 13
    • 0031103593 scopus 로고    scopus 로고
    • The global stability of a class of second order differential equations
    • Jiang J.F. The global stability of a class of second order differential equations. Nonlinear Anal 28 (1997) 855-870
    • (1997) Nonlinear Anal , vol.28 , pp. 855-870
    • Jiang, J.F.1
  • 14
    • 1642438001 scopus 로고    scopus 로고
    • Global asymptotic stability of non-autonomous systems of Lienard type
    • Jitsuro S., and Yusuke A. Global asymptotic stability of non-autonomous systems of Lienard type. J. Math. Anal. Appl. 289 2 (2004) 673-690
    • (2004) J. Math. Anal. Appl. , vol.289 , Issue.2 , pp. 673-690
    • Jitsuro, S.1    Yusuke, A.2
  • 15
    • 0041965186 scopus 로고
    • A simple boundedness theorem for a Liénard equation with damping
    • Kato J.A. A simple boundedness theorem for a Liénard equation with damping. Ann. Polon. Math. 51 (1990) 183-188
    • (1990) Ann. Polon. Math. , vol.51 , pp. 183-188
    • Kato, J.A.1
  • 16
    • 4243096687 scopus 로고    scopus 로고
    • Stability and existence of periodic solutions and almost periodic solutions on Lienard systems
    • Lin F. Stability and existence of periodic solutions and almost periodic solutions on Lienard systems. Ann. Differential Equations 13 3 (1997) 248-253
    • (1997) Ann. Differential Equations , vol.13 , Issue.3 , pp. 248-253
    • Lin, F.1
  • 17
    • 0016962062 scopus 로고
    • Some results concerning the boundedness of solutions of Lienard equations with delay
    • Luk W.S. Some results concerning the boundedness of solutions of Lienard equations with delay. SIAM J. Appl. Math. 30 4 (1976) 768-774
    • (1976) SIAM J. Appl. Math. , vol.30 , Issue.4 , pp. 768-774
    • Luk, W.S.1
  • 18
    • 34248543337 scopus 로고    scopus 로고
    • Boundedness of solutions for Liénard type equations
    • Muresan M. Boundedness of solutions for Liénard type equations. Mathematica 40 63 2 (1998) 243-257
    • (1998) Mathematica , vol.40 63 , Issue.2 , pp. 243-257
    • Muresan, M.1
  • 19
    • 84972553777 scopus 로고
    • Ultimate boundedness of solutions for a generalized Liénard equation with forcing term
    • Nakajima F. Ultimate boundedness of solutions for a generalized Liénard equation with forcing term. Tohoku Math. J. (2) 46 3 (1994) 295-310
    • (1994) Tohoku Math. J. , vol.2 46 , Issue.3 , pp. 295-310
    • Nakajima, F.1
  • 20
    • 18344387263 scopus 로고    scopus 로고
    • Boundedness and global asymptotic stability of the forced Lienard equation
    • Nápoles V., and Juan E. Boundedness and global asymptotic stability of the forced Lienard equation. Rev. Un. Mat. Argentina 41 4 (2001) 47-59
    • (2001) Rev. Un. Mat. Argentina , vol.41 , Issue.4 , pp. 47-59
    • Nápoles, V.1    Juan, E.2
  • 21
    • 38249033579 scopus 로고
    • On the boundedness of solutions of the generalized Liénard equation without the signum condition
    • Sugie J. On the boundedness of solutions of the generalized Liénard equation without the signum condition. Nonlinear Anal 11 12 (1987) 1391-1397
    • (1987) Nonlinear Anal , vol.11 , Issue.12 , pp. 1391-1397
    • Sugie, J.1
  • 22
    • 0001495944 scopus 로고    scopus 로고
    • On global asymptotic stability of systems of Liénard type
    • Sugie J., Chen D.L., and Matsunaga H. On global asymptotic stability of systems of Liénard type. J. Math. Anal. Appl. 219 1 (1998) 140-164
    • (1998) J. Math. Anal. Appl. , vol.219 , Issue.1 , pp. 140-164
    • Sugie, J.1    Chen, D.L.2    Matsunaga, H.3
  • 23
    • 1642438001 scopus 로고    scopus 로고
    • Global asymptotic stability of nonautonomous systems of Liénard type
    • Sugie J., and Amano Y. Global asymptotic stability of nonautonomous systems of Liénard type. J. Math. Anal. Appl. 289 2 (2004) 673-690
    • (2004) J. Math. Anal. Appl. , vol.289 , Issue.2 , pp. 673-690
    • Sugie, J.1    Amano, Y.2
  • 24
    • 34248203613 scopus 로고    scopus 로고
    • Boundedness and global asymptotic behavior of solutions to the Liénard equation
    • Yang Q.G. Boundedness and global asymptotic behavior of solutions to the Liénard equation. J. Systems Sci. Math. Sci. 19 2 (1999) 211-216
    • (1999) J. Systems Sci. Math. Sci. , vol.19 , Issue.2 , pp. 211-216
    • Yang, Q.G.1
  • 26
    • 38249004229 scopus 로고
    • Boundedness and stability of solutions of the retarded Liénard equation with negative damping
    • Zhang B. Boundedness and stability of solutions of the retarded Liénard equation with negative damping. Nonlinear Anal 20 3 (1993) 303-313
    • (1993) Nonlinear Anal , vol.20 , Issue.3 , pp. 303-313
    • Zhang, B.1
  • 27
    • 34248515360 scopus 로고    scopus 로고
    • On the stability and boundedness of solutions for the retarded Lienard-type equation
    • Zhou J., and Xiang L. On the stability and boundedness of solutions for the retarded Lienard-type equation. Ann. Differential Equations 15 4 (1999) 460-465
    • (1999) Ann. Differential Equations , vol.15 , Issue.4 , pp. 460-465
    • Zhou, J.1    Xiang, L.2
  • 28
    • 34248538073 scopus 로고    scopus 로고
    • The global asymptotic behavior of solutions for a nonautonomous generalized Liénard system
    • Zhou J., and Liu Z.R. The global asymptotic behavior of solutions for a nonautonomous generalized Liénard system. J. Math. Res. Exposition 21 3 (2001) 410-414
    • (2001) J. Math. Res. Exposition , vol.21 , Issue.3 , pp. 410-414
    • Zhou, J.1    Liu, Z.R.2
  • 29
    • 18744414989 scopus 로고    scopus 로고
    • On the boundedness of solutions of the vector Liénard equation
    • Wiandt T. On the boundedness of solutions of the vector Liénard equation. Dynam. Systems Appl. 7 1 (1998) 141-143
    • (1998) Dynam. Systems Appl. , vol.7 , Issue.1 , pp. 141-143
    • Wiandt, T.1


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