On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations

Steven B. Bank

Rendiconti del Seminario Matematico della Università di Padova (1991)

  • Volume: 85, page 1-25
  • ISSN: 0041-8994

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Bank, Steven B.. "On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations." Rendiconti del Seminario Matematico della Università di Padova 85 (1991): 1-25. <http://eudml.org/doc/108216>.

@article{Bank1991,
author = {Bank, Steven B.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {linear differential equations; oscillation; asymptotic expansions; higher-order equation; Hille; logarithmic differential field of rank zero},
language = {eng},
pages = {1-25},
publisher = {Seminario Matematico of the University of Padua},
title = {On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations},
url = {http://eudml.org/doc/108216},
volume = {85},
year = {1991},
}

TY - JOUR
AU - Bank, Steven B.
TI - On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1991
PB - Seminario Matematico of the University of Padua
VL - 85
SP - 1
EP - 25
LA - eng
KW - linear differential equations; oscillation; asymptotic expansions; higher-order equation; Hille; logarithmic differential field of rank zero
UR - http://eudml.org/doc/108216
ER -

References

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  1. [1] S. Bank, A note on the location of complex zeros of solutions of linear differential equations, Bull. Amer. Math. Soc. (New Series), 18 (1988), pp. 35-38. Zbl0669.34011MR919655
  2. [2] S. Bank, A note on the rate of growth of solutions of algebraic differential equations in sectors, J. London Math. Soc. (2), 1 (1969), pp. 145-154. Zbl0182.11403MR249716
  3. [3] S. Bank, On principal solutions of linear differential equations, Proc. Amer. Math. Soc., 10 (1968), pp. 724-732. Zbl0157.14204MR252727
  4. [4] S. Bank, On determining the location of complex zeros of solutions of certain linear differentiaL equations, Ann. Mat. Pura Appl., 151 (1988), pp. 67-96. Zbl0662.34005MR964503
  5. [5] S. Bank, On the instability theory of differential polynomials, Ann. Math. Pura Appl., 74 (1966), pp. 83-112. Zbl0149.29702MR204785
  6. [6] S. Bank, On zero-free regions for solutions of n-th order linear differential equations, Comment. Math. Univ. St. Paul, 36 (1987), pp. 199-213. Zbl0629.34007MR919451
  7. [7] S. Bank, On the complew zeros of sotutions of linear differential equations. (To appear - Ann. Mat. Pura Appl.). Zbl0760.34007
  8. [8] E.W. Chamberlain, Families of principal solutions of ordinary differential equations, Trans. Amer. Math. Soc., 107 (1963), pp. 261-272. Zbl0121.07201MR148974
  9. [9] W.K. Hayman, The local growth of power series: a survey of the Wiman-Valiron method, Canad. Math. Bull., 17 (1974), pp. 317-358. Zbl0314.30021MR385095
  10. [10] E. Hille, Ordinary Differential Equations in the Complex Domain, Wiley, New York (1976). Zbl0343.34007MR499382
  11. [11] E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, Reading, Mass. (1969). Zbl0179.40301MR249698
  12. [12] E. Hille, Analytic Function Theory, Volume II, Chelsea, New York (1973). Zbl0273.30002
  13. [13] R. Nevanlinna, Über Riemannsche Flächen mit endlich vielen Windungspunkten, Acta Math., 58 (1932), pp. 295-373. Zbl0004.35504MR1555350JFM58.0369.01
  14. [14] C. Powder, On the asymptotic behavior of a fundamentaL set of solutions, Trans. Amer. Math. Soc., 255 (1979), pp. 91-110. Zbl0419.34053MR542872
  15. [15] Y. Sibuya, Global Theory of a Linear Second Order Differential Equation with a Polynomial Coefficient, North Holland Math. Studies n. 18, North Holland, Amsterdam (1975). Zbl0322.34006
  16. [16] W. Strodt, Contributions to the asymptotic theory of ordinary differential equations in the complex domain, Mem. Amer. Math. Soc., n. 13 (1954). Zbl0059.07701MR67290
  17. [17] W. Strodt, Principal solutions of ordinary differential equations in the complex domain, Mem. Amer. Math. Soc., n. 26 (1957). Zbl0101.30003MR92901
  18. [18] W. Strodt, On the algebraic closure of certain partially ordered fields, Trans. Amer. Math. Soc., 105 (1962), pp. 229-250. Zbl0113.03301MR140514
  19. [19] E.C. Titchmarsh, The Theory of Functions, Oxford University Press, London, 1939. Zbl0022.14602JFM65.0302.01
  20. [20] G. Valiron, Fonctions analytiques et equations differentielles, J. Math. Pures Appl., 31 (1952), pp. 293-303. Zbl0047.31003MR51915
  21. [21] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York (1965). Zbl0133.35301MR203188
  22. [22] H. Wittich, Eindeutige Lösungen der Differentialgeichung w' = R(z, w), Math. Z., 74 (1960), pp. 278-288. Zbl0091.26102MR120413

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