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A survey of global properties of linear differential equations of the n-th order

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References

  1. Birkhoff, G. D.: On the solutions of ordinary linear homogeneous differential equations of the third order, Annals of Math. 12 (1910/11), 103–124.

    Article  MathSciNet  MATH  Google Scholar 

  2. Borůvka, O.: Linear Differentialtransformationen 2. Ordnung, VEB, Berlin 1967; Linear Differential Transformations of the Second Order, The English Univ. Press, London 1971.

    MATH  Google Scholar 

  3. Borůvka, O.: Teorija global'nych svojstv obyknovennych linejnych differencial'nych uravněnij vtorogo porjadka, Differencial'nyje uravněnija 12 (1976), 1347–1383.

    Google Scholar 

  4. Borůvka, O.: Algebraic methods in the theory of global properties of the oscillatory equations Y″ = Q(t)Y. Equadiff IV-Proceedings, Prague 1977, Lecture Notes in Mathematics 703, 35–45.

    Google Scholar 

  5. Borůvka, O.: Sur une classe des groupes continus à un paramètre formés des fonctions réelles d'une variable, Ann. Polon. Math., to appear.

    Google Scholar 

  6. Cartan, É.: La théorie des groupes finis et la géométrie différentielle traitées par la méthode du repère mobile, Gauthier-Villars, 1937.

    Google Scholar 

  7. Dolan, J. M.: On the relationship between the oscilatory behavior of a linear third-order differential equation and its adjoint, J. Diff. Equations 7 (1970), 367–388.

    Article  MathSciNet  MATH  Google Scholar 

  8. Everitt, W. N.: A note of the Dirichlet conditions for second-order differential expressions, Canad. J. Math. 28 (1976), 312–320.

    Article  MathSciNet  MATH  Google Scholar 

  9. Everitt, W. N.: On the transformation theory of ordinary second-order linear symmetric differential equations, preprint.

    Google Scholar 

  10. Guggenheimer, H.: Distribution of zeros and limit behavior of solutions of differential equations, Proc. AMS 61 (1976), 275–279.

    Article  MathSciNet  MATH  Google Scholar 

  11. Halphen, G. H.: Mémoire sur la réduction des équations différentilles linéaires aux formes intégrables. Mémoires présentés par divers savants à l'académie des sciences de l'institut de France 28 (1884), 1–301.

    Google Scholar 

  12. Hasse, M., Michler, L.: Theorie der Kategorien, VEB, Berlin 1966.

    MATH  Google Scholar 

  13. Hustý, Z.: Die Iteration homogener linearer Differentialgleichungen, Publ. Fac. Sci. Univ. J. E. Purkyně (Brno), 449 (1964), 23–56.

    MathSciNet  MATH  Google Scholar 

  14. Kummer, E. E.: De generali quadam aequatione differentiali tertii ordinis. Progr. Evang. Königl. & Stadtgymnasiums Liegnitz 1834.

    Google Scholar 

  15. Neuman, F.: Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient, Ann. Mat. Pura Appl. 75 (1967), 385–396.

    Article  MathSciNet  MATH  Google Scholar 

  16. Neuman, F.: Relation between the distribution of the zeros of the solutions of a 2nd order linear differential equation and the boundedness of these solutions, Acta Math. Acad. Sci. Hungar. 19 (1968), 1–6.

    Article  MathSciNet  Google Scholar 

  17. Neuman, F.: An explicit form of the differential equations y″ = q(t)y with periodic solutions, Ann. Mat. Pura Appl. 85 (1970), 205–300.

    Article  MathSciNet  MATH  Google Scholar 

  18. Neuman, F.: Linear differential equations of the second order and their applications, Rend. Mat. 4 (1971), 559–617.

    MathSciNet  MATH  Google Scholar 

  19. Neuman, F.: A note on Santaló's isoperimetric theorem, Revista Mat. Fis. Teor. Tucuman, 21 (1971), 203–206.

    MathSciNet  MATH  Google Scholar 

  20. Neuman, F.: Geometrical approach to linear differential equations of the n-th order, Rend. Mat. 5 (1972), 579–602.

    MathSciNet  MATH  Google Scholar 

  21. Neuman, F.: Distribution of zeros of solutions of y″ = q(t)y in relation to their behaviour in large, Studia Sci. Math. Hungar. 8 (1973), 177–185.

    MathSciNet  MATH  Google Scholar 

  22. Neuman, F.: On n-dimensional closed curves and periodic solutions of linear differential equations of the n-th order, Demonstratio Math. 6 (1973), part I, 329–337.

    MathSciNet  MATH  Google Scholar 

  23. Neuman, F.: On a problem of transformations between limit-circle and limit-point differential equations, Proc. Roy. Soc. Edinburgh, Sect. A. 72 (1973/74), 187–193.

    MathSciNet  MATH  Google Scholar 

  24. Neuman, F.: On two problems about oscillation of linear differential equations of the third order, J. Diff. Equations 15 (1974), 589–596.

    Article  MathSciNet  MATH  Google Scholar 

  25. Neuman, F.: On solutions of the vector functional equation y(ξ (x)) = f(x).A.y(x), Aequationes Math. 16 (1977), 245–257.

    Article  MathSciNet  MATH  Google Scholar 

  26. Neuman, F.: Categorial approach to global transformations of the n-th order linear differential equations, Časopis Pěst. Mat. 102 (1977), 350–355.

    MathSciNet  MATH  Google Scholar 

  27. Neuman, F.: Limit circle classification and boundedness of solutions, Proc. Roy. Soc. Edinburgh, 81 A (1978), 31–34.

    Article  MathSciNet  MATH  Google Scholar 

  28. Neuman, F.: Invarianty linejnych differencial'nych uravnenij 3-go porjadka i metod podvižnogo repera E. Kartana, Differencial'nyje uravnenija XIV (1979), 398–404.

    MathSciNet  Google Scholar 

  29. Neuman, F.: Global theory of linear differential equations of the n-th order, Proceedings of the Colloquium on Qualitative Theory of Differential Equations, August 79, Szeged-Hungary, Seria Colloquia Mathematica Societatis János Bolyai & North-Holland Publishing Company, 777–794.

    Google Scholar 

  30. Neuman, F.: Second order linear differential systems, Ann. Sci, École Norm. Super. (Paris) 13 (1980), 437–449.

    MathSciNet  MATH  Google Scholar 

  31. Neuman, F.: Global canonical forms of linear differential equations, Math. Slovaca, to appear.

    Google Scholar 

  32. Sansone, G.: Studi sulle equazioni differenziali lineari omogenee di terzo ordine nel campo reale. Revista Mat. Fis. Teor. Tucuman 6 (1948), 195–253.

    MathSciNet  MATH  Google Scholar 

  33. Stäckel, P.: Über Transformationen von Differentialgleichungen. J. Reine Angew. Math. (Crelle Journal) 111 (1893), 290–302.

    MATH  Google Scholar 

  34. Wilczynski, E. J.: Projective Differential Geometry of Curves and Ruled Surfaces, Teubner, Leipzig 1906.

    MATH  Google Scholar 

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W.N. Everitt B.D. Sleeman

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© 1982 Springer-Verlag

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Neuman, F. (1982). A survey of global properties of linear differential equations of the n-th order. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065025

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  • DOI: https://doi.org/10.1007/BFb0065025

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  • Print ISBN: 978-3-540-11968-5

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