메뉴 건너뛰기




Volumn 47, Issue 4-5, 2004, Pages 751-765

Interval oscillation criteria for second-order nonlinear perturbed differential equations

Author keywords

Integral averaging technique; Interval criteria; Oscillation; Perturbed

Indexed keywords

BOUNDARY CONDITIONS; CONFORMAL MAPPING; FUNCTIONS; INTEGRAL EQUATIONS; INTEGRATION; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; THEOREM PROVING;

EID: 1842832869     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(04)90062-4     Document Type: Article
Times cited : (5)

References (29)
  • 1
    • 0002086419 scopus 로고
    • Oscillation theorems for a second order damped nonlinear differential equation
    • J.W. Baker, Oscillation theorems for a second order damped nonlinear differential equation, SIAM J. Math. Anal. 25, 37-40, (1973).
    • (1973) SIAM J. Math. Anal. , vol.25 , pp. 37-40
    • Baker, J.W.1
  • 2
    • 0000360854 scopus 로고
    • Oscillation of solutions of damped nonlinear differential equations
    • L.E. Bobisud, Oscillation of solutions of damped nonlinear differential equations, SIAM. J. Math. Anal. 18, 601-606, (1970).
    • (1970) SIAM. J. Math. Anal. , vol.18 , pp. 601-606
    • Bobisud, L.E.1
  • 3
    • 0000158708 scopus 로고
    • The oscillatory behavior of a second order nonlinear differential equation with damping
    • G.J. Butler, The oscillatory behavior of a second order nonlinear differential equation with damping, J. Math. Anal. Appl. 57, 273-289, (1977).
    • (1977) J. Math. Anal. Appl. , vol.57 , pp. 273-289
    • Butler, G.J.1
  • 4
    • 84967790448 scopus 로고
    • Riccati techniques and variational principles in oscillation theory for linear systems
    • G.J. Butler, L.H. Erbe and A.B. Mingarelli, Riccati techniques and variational principles in oscillation theory for linear systems, Trans. Amer. Math. Soc. 303, 263-282, (1987).
    • (1987) Trans. Amer. Math. Soc. , vol.303 , pp. 263-282
    • Butler, G.J.1    Erbe, L.H.2    Mingarelli, A.B.3
  • 5
    • 0002413209 scopus 로고
    • Stability of (ru′)′ + af(u)g(u′) = 0
    • T.A. Burton and R.C. Grimmer, Stability of (ru′)′ + af(u)g(u′) = 0, Monatsh. Math. 74, 211-222, (1970).
    • (1970) Monatsh. Math. , vol.74 , pp. 211-222
    • Burton, T.A.1    Grimmer, R.C.2
  • 6
    • 33646970628 scopus 로고
    • Weighted means and oscillation conditions for second order matrix differential equations
    • R. Byers, B.J. Harri and M.K. Kwong, Weighted means and oscillation conditions for second order matrix differential equations, J. Differential Equations 61, 164-177, (1986).
    • (1986) J. Differential Equations , vol.61 , pp. 164-177
    • Byers, R.1    Harri, B.J.2    Kwong, M.K.3
  • 7
    • 84966251003 scopus 로고
    • An oscillation criterion for a forced second order linear differential equations
    • M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equations, Proc. Amer. Math. Soc. 118, 813-817, (1993).
    • (1993) Proc. Amer. Math. Soc. , vol.118 , pp. 813-817
    • El-Sayed, M.A.1
  • 8
    • 0001466802 scopus 로고
    • Oscillation theorems for nonlinear differential equations of second order
    • S.R. Grace, Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl. 171, 220-241, (1992).
    • (1992) J. Math. Anal. Appl. , vol.171 , pp. 220-241
    • Grace, S.R.1
  • 9
    • 84985381643 scopus 로고
    • Oscillation theorems for certain second order perturbed nonlinear differential equations
    • S.R. Grace and B.S. Lalli, Oscillation theorems for certain second order perturbed nonlinear differential equations, J. Math. Anal. Appl. 77, 205-214, (1980).
    • (1980) J. Math. Anal. Appl. , vol.77 , pp. 205-214
    • Grace, S.R.1    Lalli, B.S.2
  • 10
    • 0025446693 scopus 로고
    • Integral averaging technique for the oscillation of second order nonlinear differential equations
    • S.R. Grace and B.S. Lalli, Integral averaging technique for the oscillation of second order nonlinear differential equations, J. Math. Anal. Appl. 149, 277-311, (1990).
    • (1990) J. Math. Anal. Appl. , vol.149 , pp. 277-311
    • Grace, S.R.1    Lalli, B.S.2
  • 11
    • 0000104053 scopus 로고
    • Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term
    • S.R. Grace, B.S. Lalli and C.C. Yeh, Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM J. Math. Anal. 15, 1082-1093, (1984).
    • (1984) SIAM J. Math. Anal. , vol.15 , pp. 1082-1093
    • Grace, S.R.1    Lalli, B.S.2    Yeh, C.C.3
  • 12
    • 0000889295 scopus 로고
    • Asymptotic behavior of solutions of a second order nonlinear differential equation
    • J.R. Graef and P.W. Spikes, Asymptotic behavior of solutions of a second order nonlinear differential equation, J. Differential Equations 17, 451-476, (1975).
    • (1975) J. Differential Equations , vol.17 , pp. 451-476
    • Graef, J.R.1    Spikes, P.W.2
  • 13
    • 0001938157 scopus 로고
    • Boundedness and convergence to zeros of solutions of a forced second order nonlinear differential equations
    • J.R. Graef and P.W. Spikes, Boundedness and convergence to zeros of solutions of a forced second order nonlinear differential equations, J. Math. Anal. Appl. 62, 295-309, (1978).
    • (1978) J. Math. Anal. Appl. , vol.62 , pp. 295-309
    • Graef, J.R.1    Spikes, P.W.2
  • 14
    • 0001938156 scopus 로고
    • Oscillation theorems for perturbed nonlinear differential equations
    • J.R. Graef, S.M. Rankin and P.W. Spikes, Oscillation theorems for perturbed nonlinear differential equations, J. Math. Anal. Appl. 65, 375-390, (1978).
    • (1978) J. Math. Anal. Appl. , vol.65 , pp. 375-390
    • Graef, J.R.1    Rankin, S.M.2    Spikes, P.W.3
  • 15
    • 0000632529 scopus 로고
    • On nonoscillatory linear differential equations of second order
    • P. Hartman, On nonoscillatory linear differential equations of second order, Amer. J. Math. 74, 389-400, (1952).
    • (1952) Amer. J. Math. , vol.74 , pp. 389-400
    • Hartman, P.1
  • 16
    • 0031152630 scopus 로고    scopus 로고
    • Oscillation and nonoscillation for second order linear differential equations
    • C.C. Huang, Oscillation and nonoscillation for second order linear differential equations, J. Math. Anal. Appl. 210, 712-723, (1997).
    • (1997) J. Math. Anal. Appl. , vol.210 , pp. 712-723
    • Huang, C.C.1
  • 17
    • 0001003339 scopus 로고
    • Oscillation criteria related to averaging of solutions of second order differential equations (in Russian)
    • I.V. Kamenev, Oscillation criteria related to averaging of solutions of second order differential equations (in Russian), Differentsial'nye Uravnenyia 10, 246-252, (1974).
    • (1974) Differentsial'nye Uravnenyia , vol.10 , pp. 246-252
    • Kamenev, I.V.1
  • 18
    • 0001221098 scopus 로고    scopus 로고
    • Interval criteria for oscillation of second-order linear ordinary differential equations
    • Q. Kong, Interval criteria for oscillation of second-order linear ordinary differential equations, J. Math. Anal. Appl. 229, 258-270, (1999).
    • (1999) J. Math. Anal. Appl. , vol.229 , pp. 258-270
    • Kong, Q.1
  • 19
    • 0001364219 scopus 로고    scopus 로고
    • Oscillation of certain second-order nonlinear differential equations
    • W.T. Li, Oscillation of certain second-order nonlinear differential equations, J. Math. Anal. Appl. 217, 1-14, (1998).
    • (1998) J. Math. Anal. Appl. , vol.217 , pp. 1-14
    • Li, W.T.1
  • 20
    • 0034230868 scopus 로고    scopus 로고
    • Interval oscillation criteria for second order nonlinear differential equations with damping
    • W.T. Li and R.P. Agarwal, Interval oscillation criteria for second order nonlinear differential equations with damping, Computers Math. Applic. 40 (2/3), 217-230, (2000).
    • (2000) Computers Math. Applic. , vol.40 , Issue.2-3 , pp. 217-230
    • Li, W.T.1    Agarwal, R.P.2
  • 21
    • 0034179297 scopus 로고    scopus 로고
    • Interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations
    • W.T. Li and R.P. Agarwal, Interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations, J. Math. Anal. Appl. 245, 171-188, (2000).
    • (2000) J. Math. Anal. Appl. , vol.245 , pp. 171-188
    • Li, W.T.1    Agarwal, R.P.2
  • 22
    • 0011890149 scopus 로고    scopus 로고
    • Oscillation criteria for second order nonlinear differential equations with damping term
    • W.T. Li, M.Y. Zhang and X.L. Fei, Oscillation criteria for second order nonlinear differential equations with damping term, Indian J. Pure Appl. Math. 30 (10), 1017-1029, (1999).
    • (1999) Indian J. Pure Appl. Math. , vol.30 , Issue.10 , pp. 1017-1029
    • Li, W.T.1    Zhang, M.Y.2    Fei, X.L.3
  • 23
    • 34249969865 scopus 로고
    • Oscillation theorems for linear differential equations of second order
    • Ch.G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math. (Basel) 53, 482-492, (1989).
    • (1989) Arch. Math. (Basel) , vol.53 , pp. 482-492
    • Philos, Ch.G.1
  • 24
    • 0031275102 scopus 로고    scopus 로고
    • Oscillation criteria for second order nonlinear perturbed differential equations
    • Y.V. Rogovchenko, Oscillation criteria for second order nonlinear perturbed differential equations, J. Math. Anal. Appl. 215, 334-357, (1997)
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 334-357
    • Rogovchenko, Y.V.1
  • 25
    • 0001700504 scopus 로고
    • A criterion of oscillatory stability
    • A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7, 115-117, (1949).
    • (1949) Quart. Appl. Math. , vol.7 , pp. 115-117
    • Wintner, A.1
  • 26
    • 0030094401 scopus 로고    scopus 로고
    • Oscillatory behavior of solutions of certain second order nonlinear differential equations
    • P.J.Y. Wong and R.P. Agarwal, Oscillatory behavior of solutions of certain second order nonlinear differential equations, J. Math. Anal. Appl. 198, 337-354, (1996).
    • (1996) J. Math. Anal. Appl. , vol.198 , pp. 337-354
    • Wong, P.J.Y.1    Agarwal, R.P.2
  • 27
    • 84968484532 scopus 로고    scopus 로고
    • Oscillation theorems for second order linear differential equations with damping term
    • J.R. Yan, Oscillation theorems for second order linear differential equations with damping term, Proc. Amer. Math. Soc. 98, 276-282, (1996).
    • (1996) Proc. Amer. Math. Soc. , vol.98 , pp. 276-282
    • Yan, J.R.1
  • 28
    • 84966205417 scopus 로고
    • Oscillation theorems for nonlinear second order differential equations with damping term
    • C.C. Yeh, Oscillation theorems for nonlinear second order differential equations with damping term, Proc. Amer. Math. Soc. 84, 397-402, (1982).
    • (1982) Proc. Amer. Math. Soc. , vol.84 , pp. 397-402
    • Yeh, C.C.1
  • 29
    • 38249023005 scopus 로고
    • Oscillation criteria for second order nonlinear perturbed differential equations
    • C.C. Yeh, Oscillation criteria for second order nonlinear perturbed differential equations, J. Math. Anal. Appl. 138, 157-165, (1989).
    • (1989) J. Math. Anal. Appl. , vol.138 , pp. 157-165
    • Yeh, C.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.