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Boundedness theorems for certain general second order non-linear differential equations

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References

  1. T. Dlotko, “Quelques théorèmes sur les intégrales bornées de certaines équations différentielles ordinaires du second ordre”, Annales Polonici MathematiciX (1961), 151–159. MR # 24-1466.

    Google Scholar 

  2. M. Ia. Leonov, “On quasiharmonic oscillations”, PMM vol.10, Nos. 5–6, (1946) 575–580 (Russian). MR # 8-329.

    Google Scholar 

  3. Ju. A. Klokoff, “Some theorems on boundedness of solutions of ordinary differential equations”, Uspehi Mat. Nauk,13 (1958), No. 2 (80), 189–194; English translation, Chinese mathematics3 (1963), 34–41. MR # 20-2527.

    Google Scholar 

  4. P. Waltman, “Some properties of solutions ofu″(t)+a(t) f(u)=0”, Monatshefte für Mathematik,67 (1963), 50–54. MR # 26-5214.

    Google Scholar 

  5. H. Hochstadt, “On the stability of certain second order differential equations”, SIAM Journal,12 (1964), 58–59. MR # 28-5224.

    Google Scholar 

  6. J. S. W. Wong, “A note on boundedness theorems of certain second order differential equations”, SIAM Review6 (1964), 175–176. MR # 30-308.

    Google Scholar 

  7. J. S. W. Wong andT. A. Burton, “Some properties of solutions ofu″(t)+a(t) f(u) g(u′)=0 (II)”, Monatshefte für Mathematik,69 (1965), 368–374.

    Google Scholar 

  8. J. S. W. Wong, “Some properties of solutions ofu″(t)+a(t) f(u) g(u′)=0 (III)”, SIAM Journal,14 (1966), 209–214.

    Google Scholar 

  9. J. S. W. Wong, “Boundedness theorems for solutions ofu″(t)+a(t) f(u) g(u′)=0 (IV)”, (to appear).

  10. R. Bellman, Stability theory of ordinary differential equations, McGraw-Hill, New York, 1953.

    Google Scholar 

  11. V. M. Starzhinskii, “Sufficient conditions of stability of a mechanical system with one degree of freedom”, PMM vol.16, Nr. 3, (1952), 369–374 (Russian). MR # 13-944.

    Google Scholar 

  12. N. P. Kuptsov, “On a sufficient condition for the stability of the trivial solution of a system of two linear differential equations”, PMM vol.25, No. 4 (1961), 791–793. (English Translation PMM 25:4 (1961), 1181–1186). MR # 25-3242.

    Google Scholar 

  13. J. La Salle andS. Lefschetz, Stability by Liapunov's Direct Method (with applications), Academic Press, New York, 1961.

    Google Scholar 

  14. A. L. Ruiz, “Unstable characteristics of a class of functions defined by a linear differential equation with periodic coefficients”, SIAM Journal,11 (1963), 148–158. MR # 27-1659.

    Google Scholar 

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Wong, J.S.W. Boundedness theorems for certain general second order non-linear differential equations. Monatshefte für Mathematik 71, 80–86 (1967). https://doi.org/10.1007/BF01299962

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