Comparison theorems for functional differential equations with deviating arguments

Takasi KUSANO; Manabu NAITO

doi:10.2969/jmsj/03330509

Takasi KUSANO, Manabu NAITO

著者情報

ジャーナルフリー

1981 年 33 巻 3 号 p. 509-532

DOI https://doi.org/10.2969/jmsj/03330509

詳細

Published: 1981 Received: 1979/11/05 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J.J.A.M. Brands, Oscillation theorems for second-order functional differential equations, J. Math. Anal. Appl., 63 (1978), 54-64.
2) T.A. Canturija, On a comparison theorem for linear differential equations, Izv. Akad. Nauk SSSR, Ser. Mat., 40 (1976), 1128-1142. (Russian)
3) T. A. Canturija, Some comparison theorem for higher order ordinary differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 25 (1977), 749-756. (Russian)
4) T. A. Canturija, On some asymptotic properties of solutions of linear ordinary differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 25 (1977), 757-762.
5) L. Erbe, Oscillation criteria for second order nonlinear delay equations, Canad. Math. Bull., 16 (1973), 49-56.
6) L. Erbe, Oscillation and asymptotic behavior of solutions of third order differential delay equations, SIAM J. Math. Anal., 7 (1976), 491-500.
7) K. E. Foster and R. C. Grimmer, Nonoscillatory solutions of higher order delay equations, J. Math. Anal. Appl., 77 (1980), 150-164.
8) R. C. Grimmer, Oscillation criteria and growth of nonoscillatory solutions of even order ordinary and delay-differential equations, Trans. Amer. Math. Soc., 198 (1974), 215-228.
9) A. G. Kartsatos, On n-th order differential inequalities, J. Math. Anal. Appl., 52 (1975), 1-9.
10) A. G. Kartsatos and H. Onose, A comparison theorem for functional differential equations, Bull. Austral. Math. Soc., 14 (1976), 343-347.
11) I. T. Kiguradze, On the oscillation of solutions of the equation d_mu/dt_m+a(t) |u|_n sign u=0, Mat. Sb., 65 (1964), 172-187. (Russian)
12) Y. Kitamura and T. Kusano, Nonlinear oscillation of higher-order functional differential equations with deviating arguments, J. Math. Anal. Appl., 77 (1980), 100-119.
13) V. A. Kondrat'ev, On the oscillation of solutions of the equation y⁽ⁿ⁾+p(x)y=0, Trudy Moskov Mat. Obšc., 10 (1961), 419-436. (Russian)
14) K. Kreith, T. Kusano and M. Naito, Oscillation criteria for weakly superlinear differential equations of even order, J. Differential Equations, 38 (1980), 32-40.
15) T. Kusano and M. Naito, Oscillation and nonoscillation theorems for second order retarded differential equations (manuscript).
16) T. Kusano and M. Naito, Nonlinear oscillation of second order differential equations with retarded argument, Ann. Mat. Pura Appl. Ser. 4, 106 (1975), 171-185.
17) T. Kusano and M. Naito, Oscillation criteria for general linear ordinary differential equations, Pacific J. Math., 92 (1981).
18) T. Kusano and N. Yoshida, Oscillation criteria for a fourth order linear elliptic equation, (manuscript).
19) D.L. Lovelady, An asymptotic analysis of an odd order linear differential equation, Pacific J. Math., 57 (1975), 475-480.
20) D.L. Lovelady, Oscillation and a class of odd order linear differential equations, Hiroshima Math. J., 5 (1975), 371-383.
21) D. L. Lovelady, Oscillation and even order linear differential equations, Rocky Mountain J. Math., 6 (1976), 299-304.
22) D.L. Lovelady, An asymptotic analysis of an even order linear differential equation, Funkcial. Ekvac., 19 (1976), 133-138.
23) D. L. Lovelady, Oscillation and a class of linear delay differential equations, Trans. Amer. Math. Soc., 226 (1977), 345-364.
24) W.E. Mahfoud, Comparison theorems for delay differential equations, Pacific J. Math., 83 (1979), 187-197.
25) H. Onose, A comparison theorem and the forced oscillation, Bull. Austral. Math. Soc., 13 (1975), 13-19.
26) H. Onose, A comparison theorem for delay differential equations, Utilitas Math., 10 (1976), 185-191.
27) Ch. G. Philos and V.A. Staikos, Basic comparison results for the oscillatory and asymptotic behavior of differential equations with deviating arguments, Univ. Ioannina Tech. Rep., No. 12 (1978).
28) Y.G. Sficas, On the behavior of nonoscillatory solutions of differential equations with deviating argument, Nonlinear Anal., 3 (1979), 379-394.
29) K. Tanaka, Asymptotic analysis of odd order ordinary differential equations, Hiroshima Math. J., 10 (1980), 391-408.
30) W.F. Trench, Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc., 189 (1974), 319-327.

Right : [1] J. J. A. M. Brands, Oscillation theorems for second-order functional differential equations, J. Math. Anal. Appl., 63 (1978), 54-64.
[2] T. A. Canturija, On a comparison theorem for linear differential equations, Izv. Akad. Nauk SSSR, Ser. Mat., 40 (1976), 1128-1142. (Russian)
[3] T. A. Canturija, Some comparison theorem for higher order ordinary differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 25 (1977), 749-756. (Russian)
[4] T. A. Canturija, On some asymptotic properties of solutions of linear ordinary differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 25 (1977), 757-762.
[5] L. Erbe, Oscillation criteria for second order nonlinear delay equations, Canad. Math. Bull., 16 (1973), 49-56.
[6] L. Erbe, Oscillation and asymptotic behavior of solutions of third order differential delay equations, SIAM J. Math. Anal., 7 (1976), 491-500.
[7] K. E. Foster and R. C. Grimmer, Nonoscillatory solutions of higher order delay equations, J. Math. Anal. Appl., 77 (1980), 150-164.
[8] R. C. Grimmer, Oscillation criteria and growth of nonoscillatory solutions of even order ordinary and delay-differential equations, Trans. Amer. Math. Soc., 198 (1974), 215-228.
[9] A. G. Kartsatos, On n-th order differential inequalities, J. Math. Anal. Appl., 52 (1975), 1-9.
[10] A. G. Kartsatos and H. Onose, A comparison theorem for functional differential equations, Bull. Austral. Math. Soc., 14 (1976), 343-347.
[11] I. T. Kiguradze, On the oscillation of solutions of the equation d^mu/dt^m+a(t) |u|ⁿ sign u=0, Mat. Sb., 65 (1964), 172-187. (Russian)
[12] Y. Kitamura and T. Kusano, Nonlinear oscillation of higher-order functional differential equations with deviating arguments, J. Math. Anal. Appl., 77 (1980), 100-119.
[13] V. A. Kondrat'ev, On the oscillation of solutions of the equation y⁽ⁿ⁾+p(x)y=0, Trudy Moskov Mat. Obšc., 10 (1961), 419-436. (Russian)
[14] K. Kreith, T. Kusano and M. Naito, Oscillation criteria for weakly superlinear differential equations of even order, J. Differential Equations, 38 (1980), 32-40.
[15] T. Kusano and M. Naito, Oscillation and nonoscillation theorems for second order retarded differential equations (manuscript).
[16] T. Kusano and M. Naito, Nonlinear oscillation of second order differential equations with retarded argument, Ann. Mat. Pura Appl. Ser. 4, 106 (1975), 171-185.
[17] T. Kusano and M. Naito, Oscillation criteria for general linear ordinary differential equations, Pacific J. Math., 92 (1981).
[18] T. Kusano and N. Yoshida, Oscillation criteria for a fourth order linear elliptic equation, (manuscript).
[19] D. L. Lovelady, An asymptotic analysis of an odd order linear differential equation, Pacific J. Math., 57 (1975), 475-480.
[20] D. L. Lovelady, Oscillation and a class of odd order linear differential equations, Hiroshima Math. J., 5 (1975), 371-383.
[21] D. L. Lovelady, Oscillation and even order linear differential equations, Rocky Mountain J. Math., 6 (1976), 299-304.
[22] D. L. Lovelady, An asymptotic analysis of an even order linear differential equation, Funkcial. Ekvac., 19 (1976), 133-138.
[23] D. L. Lovelady, Oscillation and a class of linear delay differential equations, Trans. Amer. Math. Soc., 226 (1977), 345-364.
[24] W. E. Mahfoud, Comparison theorems for delay differential equations, Pacific J. Math., 83 (1979), 187-197.
[25] H. Onose, A comparison theorem and the forced oscillation, Bull. Austral. Math. Soc., 13 (1975), 13-19.
[26] H. Onose, A comparison theorem for delay differential equations, Utilitas Math., 10 (1976), 185-191.
[27] Ch. G. Philos and V. A. Staikos, Basic comparison results for the oscillatory and asymptotic behavior of differential equations with deviating arguments, Univ. Ioannina Tech. Rep., No. 12 (1978).
[28] Y. G. Sficas, On the behavior of nonoscillatory solutions of differential equations with deviating argument, Nonlinear Anal., 3 (1979), 379-394.
[29] K. Tanaka, Asymptotic analysis of odd order ordinary differential equations, Hiroshima Math. J., 10 (1980), 391-408.
[30] W. F. Trench, Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc., 189 (1974), 319-327.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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