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

Rendiconti del Seminario Matematico della Università di Padova (1991)

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

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topBank, 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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- [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] S. Bank, On principal solutions of linear differential equations, Proc. Amer. Math. Soc., 10 (1968), pp. 724-732. Zbl0157.14204MR252727
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- [7] S. Bank, On the complew zeros of sotutions of linear differential equations. (To appear - Ann. Mat. Pura Appl.). Zbl0760.34007
- [8] E.W. Chamberlain, Families of principal solutions of ordinary differential equations, Trans. Amer. Math. Soc., 107 (1963), pp. 261-272. Zbl0121.07201MR148974
- [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] E. Hille, Ordinary Differential Equations in the Complex Domain, Wiley, New York (1976). Zbl0343.34007MR499382
- [11] E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, Reading, Mass. (1969). Zbl0179.40301MR249698
- [12] E. Hille, Analytic Function Theory, Volume II, Chelsea, New York (1973). Zbl0273.30002
- [13] R. Nevanlinna, Über Riemannsche Flächen mit endlich vielen Windungspunkten, Acta Math., 58 (1932), pp. 295-373. Zbl0004.35504MR1555350JFM58.0369.01
- [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] 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] 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] W. Strodt, Principal solutions of ordinary differential equations in the complex domain, Mem. Amer. Math. Soc., n. 26 (1957). Zbl0101.30003MR92901
- [18] W. Strodt, On the algebraic closure of certain partially ordered fields, Trans. Amer. Math. Soc., 105 (1962), pp. 229-250. Zbl0113.03301MR140514
- [19] E.C. Titchmarsh, The Theory of Functions, Oxford University Press, London, 1939. Zbl0022.14602JFM65.0302.01
- [20] G. Valiron, Fonctions analytiques et equations differentielles, J. Math. Pures Appl., 31 (1952), pp. 293-303. Zbl0047.31003MR51915
- [21] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York (1965). Zbl0133.35301MR203188
- [22] H. Wittich, Eindeutige Lösungen der Differentialgeichung w' = R(z, w), Math. Z., 74 (1960), pp. 278-288. Zbl0091.26102MR120413

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