Index boundedness of an entire solution of a
differential equation (in Ukrainian)

Z. M. Sheremeta

For $l(x)\equiv\text{const}>1$ the boundedness of $l$-index of an entire solution of the differential equation $z^2 w''+(\beta_0 z^2+\beta_1 z) w'+(\gamma_0 z^2+\gamma_1 z+\gamma_2)w=0$ is investigated.

1. Shah S.M. Univalence of a function $f$ and its successive derivatives when $f$ satisfies a differential equation, II // J. Math. anal. and appl.-- 1989. -- V. 142. -- P. 422-430.

2. Шеремета З.М. О свойствах целых решений одного дифференциального уравнения // Дифференц. уравн. – 2000. - Т. 36, № 8. – C. 1045-1050.

3. Sheremeta Z.M. On entire solutions of a differential equation // Matematychni studii. – 2000. – Т. 14, № 1. – C. 54-58.

4. Sheremeta M.M. Analytic functions of bounded index. – Lviv: VNTL Publishers. – 1999. – 141 pp.

5. Lepson B. Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index // Proc. Sympos. Pure Math., V.2. Amer. Math. Soc., Providence, Rhode Island. – 1968. – P.298–307.

6. Shah S.M. Entire solutions of linear differential equations and bounds for growth and index numbers // Proc. of the Royal Soc of Edinburg. – 1983. – V.A94. – P.49–60.

	Index boundedness of an entire solution of a differential equation (in Ukrainian)
Author	Z. M. Sheremeta Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
Abstract	For $l(x)\equiv\text{const}>1$ the boundedness of $l$-index of an entire solution of the differential equation $z^2 w''+(\beta_0 z^2+\beta_1 z) w'+(\gamma_0 z^2+\gamma_1 z+\gamma_2)w=0$ is investigated.
Keywords	index boundedness, entire solution, differential equation
DOI	doi:10.30970/ms.19.2.208-212
Reference	1. Shah S.M. Univalence of a function $f$ and its successive derivatives when $f$ satisfies a differential equation, II // J. Math. anal. and appl.-- 1989. -- V. 142. -- P. 422-430. 2. Шеремета З.М. О свойствах целых решений одного дифференциального уравнения // Дифференц. уравн. – 2000. - Т. 36, № 8. – C. 1045-1050. 3. Sheremeta Z.M. On entire solutions of a differential equation // Matematychni studii. – 2000. – Т. 14, № 1. – C. 54-58. 4. Sheremeta M.M. Analytic functions of bounded index. – Lviv: VNTL Publishers. – 1999. – 141 pp. 5. Lepson B. Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index // Proc. Sympos. Pure Math., V.2. Amer. Math. Soc., Providence, Rhode Island. – 1968. – P.298–307. 6. Shah S.M. Entire solutions of linear differential equations and bounds for growth and index numbers // Proc. of the Royal Soc of Edinburg. – 1983. – V.A94. – P.49–60.
Pages	208-212
Volume	19
Issue	2
Year	2003
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Index boundedness of an entire solution of a differential equation (in Ukrainian)