On second order nonlinear oscillation

1 Atkinson, F. V. On second-order non-linear oscillation Pacific J. Math. 5 1955 643-647 MR0072316

3 Belohorec, S. Neoscilatoricke riešenia istej nelinéarnej diferenciàlnej rownice druhého radu Mat. Fyz. časop. Slovez Akad. Viad 12 1962 253-262 MR0159994 Cache/Be/Belohorec,Neoscilatoricke,Mat*,1962,1963

4 Bhatia, N. P. Some oscillation theorems for second order differential equations J. Math. Anal., Appl. 15 1966 442-446 MR0203164 100 Cache/Bh/Bhatia,oscillation,J*,1966,1967

5 Bihari, I. A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations Acta Math. Sci. Hungar. 7 1956 81-94 MR0079154 100 Cache/Bi/Bihari,generalization,Acta*,1956,1957

6 Bihari, I. Ausdehnung der Sturmschen Oscillations and Vergleichssatze auf die Losungen gewisser nicht-linear differential-gleichungen zweiter ordnung Magyar Tud. Acad. Mat. Kutato Int. Közl 2 1957 159-173 MR0103322 Cache/Bi/Bihari,differential-gleichungen,Magyar*,1957,1958

7 Bihari, I. Extension of certain theorems of the Sturmian type to non-linear second order differential equations Magyar Tud. Acad. Mat. Kutato Int. Kozl 3 1958 13-20 MR0103321 Cache/Bi/Bihari,non-linear,Magyar*,1958,1959

8 Bihari, I. Oscillation and monotonity theorems concerning nonlinear differential equations of the second order Acta Math. Sci. Hungar. 9 1958 83-104 MR0095321 91 Cache/Bi/Bihari,Oscillation,Acta*,1958,1959

10 Coffman, C. V.; Ullrich, D. F. On the continuation of solutions of a certain nonlinear differential equation Monatsh. Math. 71 1967 385-392 MR0227494 90 Cache/Co/Coffman,continuation,Monatsh*,1967,1968

11 Coles, W. J. An oscillation criterion for second-order linear differential equations Proc. Amer. Math. Soc. 19 1968 755-759 Data is not found in MathSci. Cache/Co/Coles,second-order,Proc*,1968,1969

13 Conti, R.; Graffi, D.; Sansone, G. The Italian contribution to the theory of nonlinear ordinary differential equations and to nonlinear mechanics during the years 1951-1961 Qualitative methods in the theory of Nonlinear vibrations, Proc. Int. Sympos. Nonlinear Vibrations II 1961 172-189 MR0183915 84 Cache/Co/Conti,contribution,*,1961,1962

15 Das, D. M. Properties of solutions of certain nonlinear differential equations J. Math. Anal. Appl. 8 1964 445-452 MR0160985 100 Cache/Da/Das,Properties,J*,1964,1965

16 Fite, W. B. Concerning the zeros of the solution of certain differential equations Trans. Amer. Math. Soc 19 1918 341-352 MR1501107 90 Cache/Fi/Fite,Concerning,Trans*,1918,1919

17 Golomb, M. Bounds for solutions of nonlinear differential stsytems Archive Rat. Mech. Anal 1 1958 272-282 MR0104015 85 Cache/Go/Golomb,solutions,Archive*,1958,1959

18 Hallam, T. G. Asymptotic behavior of the solutions of an nth order nonhomogeneous ordinary differential equations Trans. Amer. Math. Soc. 122 1966 177-194 MR0188562 92 Cache/Ha/Hallam,nonhomogeneous,Trans*,1966,1967

19 Hallam, T. G. Asymptotic expansions in a nonhomogeneous differential equation Proc. Amer. Math. Socl 18 1967 432-438 MR0212292 100 Cache/Ha/Hallam,nonhomogeneous,Proc*,1967,1968

21 Hartman, P. On linear second order differential equations with small coefficients Amer. J. Math. 73 1951 955-962 MR0045896 100 Cache/Ha/Hartman,linear,Amer*,1951,1952

22 Hartman, P. On non-oscillatory linear differential equations of second order Amer. J. Amth. 74 1952 389-400 MR0048667 100 Cache/Ha/Hartman,non-oscillatory,Amer*,1952,1953

24 Hartman, P.; Wintner, A. On the nonincreasing solutions of $y''=f(x,y,y')$ Amer. J. Math. 73 1951 390-404 MR0042004 Cache/Ha/Hartman,nonincreasing,Amer*,1951,1952

25 Hastings, S. P. Boundary Value Problems in one differential equation with a discontinuity J. Diff. Eqn. 1 1965 346-369 MR0180723 100 Cache/Ha/Hastings,discontinuity,J*,1965,1966

26 Hille, E. Non-oscillation Theorems Trans. Amer. Math. Soc. 64 1948 234-252 MR0027925 Cache/Hi/Hille,Nonoscillation,Trans*,1948,1949

27 Howard, H. C. Oscillation and nonoscillation criteria for $y''+f(y(x))p(x)=0$ Pacific J. Math. 12 1962 243-251 MR0145150 Cache/Ho/Howard,y''+f(y(x))p(x)=0,Pacific*,1962,1963

28 Jasny, M. On the existence of an oscillating solution of the nonlinear differential equation of the second order $y''+f(x)y^{2n-1}=0$ Casopis Pestovani Matematiky 85 1960 78-83 MR0142840 Cache/Ja/Jasny,y''+f(x)y^2n-1=0,Casopis*,1960,1961

29 Jones, J. Jr. On the extension of a theorem of Atkinson Quart. J. Math. 7 1956 306-309 MR0096868 87 Cache/Jo/Jones,extension,Quart*,1956,1957

30 Jones, J. Jr. On nonlinear second order differential equation Proc. Amer. Math. Soc. 9 1958 586-588 MR0104878 83 Cache/Jo/Jones,nonlinear,Proc*,1958,1959

31 Kurzweil, J. A note on oscillatory solution of equation $y''+f(x)y^{2n-1}=0$ Casopis Pestovani Matematiky 85 1960 357-358 MR0126025

32 Leighton, W. The detection of the oscillation of solutions of a second order linear differential equation Duke Math. J. 17 1950 57-62 MR0032065 100 Cache/Le/Leighton,oscillation,Duke*,1950,1951

33 Leighton, W. On self-adjoint differential equations of second order J. London Math. Soc. 27 1952 37-47 MR0046506 100 Cache/Le/Leighton,self-adjoint,J*,1952,1953

34 Locke, P. On the asymptotic behavior of solutions of an nth order nonlinear equation Proc. Amer. Math. Soc. 18 1967 383-390 MR0212293 83 Cache/Lo/Locke,asymptotic,Proc*,1967,1968

35 Macki, J. W.; Wong, J. S. W. Oscillation of solutions to second order nonlinear differential equation Pacific J. Math. 24 1968 111-117 MR0224908 75 Cache/Ma/Macki,Oscillation,Pacific*,1968,1969

37 Milne, W. E. A theorem on oscillation Bull. Amer. Math. Soc. 28 1922 102-104 Data is not found in MathSci. Cache/Mi/Milne,oscillation,Bull*,1922,1923

38 Moore, R. A. The behavior of solutions of a linear differential equation of second order Pacific J. Math. 5 1955 125-145 MR0068690 100 Cache/Mo/Moore,solutions,Pacific*,1955,1956

39 Moore, R. A.; Nehari, Z. Nonoscillation theorems for a class of nonlinear differential equation Trans. Amer. Math. Soc. 93 1959 30-52 MR0111897 Cache/Mo/Moore,Non-oscillation,Trans*,1959,1960

40 Moroney, R. M. Note on a theorem of Nehari Proc. Amer. Math. Soc. 13 1962 407-410 MR0148983 100 Cache/Mo/Moroney,theorem,Proc*,1962,1963

41 Muldowney, J. S.; Wong, J. S. W. Bounds for solutions of a nonlinear integrodifferential equations J. of Math. Anal. and Appl 23 1968 487-499 MR0238051 100 Cache/Mu/Muldowney,integrodifferential,J*,1968,1969

42 Nehari, Z. On a class of nonlinear second order differential equations Trans. Amer. Math. Soc. 95 1960 101-123 MR0111898 87 Cache/Ne/Nehari,nonlinear,Trans*,1960,1961

43 Nehari, Z. Characteristic values associated with a class of nonlinear second order differential equations Acta Math. 105 1961 141-175 MR0123775 81 Cache/Ne/Nehari,Characteristic,Acta*,1961,1962

44 Osgood, W. F. On a theorem of oscillation Bull. Amer. Math. Soc. 25 1919 216-221 Data is not found in MathSci. Cache/Os/Osgood,oscillation,Bull*,1919,1920

45 Pinter, L. Oszillationssatze fur einen Typ von nichtlinearen Differentialgleichungen zweiter ordnung Magyar Tud. Acad. Mat. Kutato Int. Közl. 6 1961 333-350 MR0148998 Cache/Pi/Pinter,Differentialgleichungen,Magyar*,1961,1962

46 Petropavlovskaya, R. V. On the oscillatory aspect of solutions of the differential equation $u''=f(u,u',t)$ Dokl. Akad. Nauk SSR 108 1956 389-391 MR0083631 100 Cache/Pe/Petropavlovskaya,u''=f(u,u',t),Dokl*,1956,1957

47 Shevelo, V. N. Problems, methods, and fundamental results in the theory of oscillation of solutions of nonlinear non-autonomous ordinary differential equations Proceedings of the 2 nd All-Union Conference on Theoretical and Applied Mechanics, Moscow 1965 142-157 Data is not found in MathSci. Cache/Sh/Shevyelo,non-autonomous,*,1965,1966

48 Shevelo, V. N.; Shtelik, V. G. Certain problems concerning the oscillation of solutions of nonlinear non-autonomous second order equations Dokl. Akad. Nauk SSSR 149 1963 276-279 MR0150387 Cache/Sh/Shevyelo,non-autonomous,Dokl*,1963,1964

49 Taam, C. T. An extension of Osgood's oscillation theorem for a nonlinear differential equation Proc. Amer. Math. Soc. 5 1954 705-715 MR0067286 Cache/Ta/Taam,oscillation,Proc*,1955,1956

50 Tomastik, E. C. Oscillation of a nonlinear second order differential equation SIAM J. 15 1967 1275-1277 MR0226115 100 Cache/To/Tomastik,Oscillation,SIAM*,1967,1968

51 Utz, W. R. Properties of solutions of $u''+g(t)u^{2n-1}=0$ Monatsh. Math 66 1962 55-60 MR0138834 Cache/Ut/Utz,u''+g(t)u^2n-1=0,Monatsh*,1962,1963

52 Utz, W. R. Properties of solutions of $u''+g(t)u^{2n-1}=0$, II Monatsh. Math. 69 1965 353-361 MR0193334 Cache/Ut/Utz,u''+g(t)u^2n-1=0,,Monatsh*,1965,1966

53 Waltman, P. Some Properties of solutions of $u''+a(t)f(u)=0$ Monatsh. Math. 67 1963 50-54 MR0147700 Cache/Wa/Waltman,u''+a(t)f(u)=0,Monatsh*,1963,1964

54 Waltman, P. Oscillation of solutions of a nonlinear equation SIAM Review 5 1963 128-130 MR0152706 100 Cache/Wa/Waltman,Oscillation,SIAM*,1963,1964

55 Waltman, P. On the asymptotic behavior of solutions of a nonlinear equation Proc. Amer. Math. Soc. 15 1964 918-923 MR0176170 100 Cache/Wa/Waltman,asymptotic,Proc*,1964,1965

56 Waltman, P. An oscillation criterion for a nonlinear second order equation J. Math. Anal. and Appl. 10 1965 439-441 MR0173050 100 Cache/Wa/Waltman,oscillation,J*,1965,1966

57 Waltman, P. On the asymptotic behavior of solutions of an $n$th order equation Monatsh. Math. 69 1965 427-430 MR0185217 83 Cache/Wa/Waltman,asymptotic,Monatsh*,1965,1966

59 Willett, D.; Wong, J. S. W. Some properties of the solutions of $(p(t)x')'+q(t)f(x)=0$ J. Math. Anal. and Appl. 23 1968 15-24 MR0226117 Cache/Wi/Willett,(p(t)x')'+q(t)f(x)=0,J*,1968,1969

60 Wintner, A. On the Laplace-Fourier transcendents occurring in mathematical physics Amer. J. Math. 69 1947 87-97 MR0019182 100 Cache/Wi/Wintner,Laplace-Fourier,Amer*,1947,1948

61 Wintner, A. A criterion of oscillatory stability Quart. J. Appl. Math. 7 1949 115-117 MR0028499 100 Cache/Wi/Wintner,oscillatory,Quart*,1949,1950

62 Wintner, A. On the non-existence of conjugate points Amer. J. Math 73 1951 368-380 MR0042005 100 Cache/Wi/Wintner,non-existence,Amer*,1951,1952

64 Wong, J. S. W.; Burton, T. A. Some properties of solutions of $u''(t)+a(t)f(u)g(u')=0$, II Monatsh. Math. 69 1965 368-374 MR0186885 Cache/Wo/Wong,u''(t)+a(t)f(u)g(u')=0,,Monatsh*,1965,1966

64 Wong, J. S. W. A note on boundedness theorems of certain second order differential equations SIAM Review 6 1964 175-176 MR0170067 100 Cache/Wo/Wong,boundedness,SIAM*,1964,1965

65 Wong, J. S. W. Some properties of solutions of $u''(t)+a(t)f(u)g(u')=0$, III SIAM Journal 14 1966 209-214 MR0203167 Cache/Wo/Wong,u''(t)+a(t)f(u)g(u')=0,,SIAM*,1966,1967

66 Wong, J. S. W. On two theorems of Waltman SIAM Journal 14 1966 724-728 MR0206409 100 Cache/Wo/Wong,theorems,SIAM*,1966,1967

67 Wong, J. S. W. Explicit Bounds for solutions of certain second order nonlinear equations J. Math. Anal. Appl. 17 1967 339-342 MR0206395 90 Cache/Wo/Wong,solutions,J*,1967,1968

68 Wong, J. S. W. Boundedness Theorems for solutions of $u''(t)+a(t)f(u)g(u')=0$, IV L'enseignment Mathematique XIII 1967 157-165 MR0234059 Cache/Wo/Wong,u''(t)+a(t)f(u)g(u')=0,,L'enseignment*,1967,1968

69 Wong, J. S. W. A note on second order nonlinear oscillation SIAM Review 10 1968 88-91 MR0227525 100 Cache/Wo/Wong,oscillation,SIAM*,1968,1969

70 Wong, J. S. W. Remarks on the asymptotic behavior of certain perturbed linear systems Glasgow Math. J. 84 MR0257491 90 Cache/Wo/Wong,asymptotic,Glasgow*,1963,1973 1970

71 Wong, J. S. W. Second order linear oscillation with integrable coefficients Bull. Amer. Math. Soc. 74 1968 909-911 MR0233010 100 Cache/Wo/Wong,coefficients,Bull*,1968,1969

1 Belohorec, S. On some properties of the equation $y''(x)+f(x)y^\alpha(x)=0$ Mat. Casopis Sloven, Akad. Vied. 17 1967 10-19 MR0214854

2 Bihari, I. An oscillation theorem concerning the halflinear differential equation of the second order Magyar Tud. Akad. Mat. Kutato Int. Kozl. 8 1963 275-280 MR0171959 90 Cache/Bi/Bihari,oscillation,Magyar*,1963,1964

7 Izjumova, D. V. On conditions for oscillation and non-oscillation for solutions of a non-linear differential equation of the second order Differential Equations 12 1966 1572-1586 (Russian) MR0209579 Cache/Iz/Izuniova,non-oscillation,Differential*,1966,1967

8 Kartsatos, A. G. Some theorems on oscillation of certain non-linear second order differential equations Arch. der Math. XVIII 1967 425-429 MR0221018 72 Cache/Ka/Kartsatos,oscillation,Arch*,1967,1968

9 Kartsatos, A. G. On oscillations of non-linear equations of second order J. Math. Anal. and Appl. 24 1968 MR0237873 87 Cache/Ka/Kartsatos,oscillations,J*,1968,1969 665-668

10 Kiguradze, I. T. On conditions for oscillation of solutions of the equation $u''+a(t)|u|^n\mathrm{sgn}u=0$ Casopis Pestovani Matematiky 87 1962 492-495 (Russian) MR0181800 Cache/Ki/Kiguradze,u''+a(t)|u|^nsgnu=0,Casopis*,1962,1963

11 Kiguradze, I. T. A note on the oscillation of solutions of the equation Casopis Pestovani Matematiky 92 1967 343-350 MR0221012 71 Cache/Ki/Kiguradze,oscillation,Casopis*,1967,1968