[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2005.42.1.203

ON FACTORIZATION OF SOLUTIONS TO SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

SHENG, WANG (College of Economics and Management, South China Agricultural University)

Publication Information

Bulletin of the Korean Mathematical Society / v.42, no.1, 2005 , pp. 203-211 More about this Journal

Abstract

If a meromorphic solution of second order homogeneous linear differential equation is factorizable, then the right factor of the factorization of the solution has order not more than the coefficient's. And some asympotic properties of solutions are studied.

Keywords

factorization; left factor; linear differential equation; meromorphic solution; right factor;

Citations & Related Records

Reference

1	I. N. Baker, The iteration of entire transcendental functions and the solution of the functional equation f (f(z)) = F(z), Math. Ann. 129 (1955), 174-180 DOI
2	S. A. Gao, Z. X. Chen and T. W. Chen, Complex oscillation theory of linear differential equations, Press of Mid China Science and Technology University, Wuhan, 1998
3	J. H. Zheng, Complex analysis (Chinese), Tsinghua University Press, Beijing, 2000
4	J. H. Zheng and Y. Z. He, On factorization of the solutions of the equation w' + A( $e^z$ )w = 0, J. Japan Math. Soc. 53 (2001), no. 4, 835-845 DOI
5	S. Wang, On some properties of Fatou and Julia sets of meromorphic functions (Chinese), PhD. Disssertation of Tsinghua University, Beijing, October, 2002
6	G. H. Zhang, Entire and meromorphic functions theory: deficient values, asymptotic values and singular directions (Chinese), Press of science, Beijing, 1986
7	G. Polya, On an integral function of an integral function, J. London Math. Soc. 1 (1926), 12-15 DOI
8	F. Gross and C. F. Osgood, A simpler proof of a theorem of Steinmetz, J. Math. Anal. Appl. 143 (1989), 290-294 DOI
9	W. K. Hayman, Meromorphic functions, Oxford University Press, London, 1964
10	W. K. Hayman, Research problems in function theory, Athlone Press, 1967
11	N. Steinmetz, Uber die faktorisierbaren Losungen gewohnlicher Differentialgleichungen, Math. Z. 170 (1980), 168-180.
12	G. Valiron, Lectures on the general theory of integral functions, Toulouse: Edouard privat, 1923