On the Complex Oscillation of Some Linear Differential Equations

✍ Scribed by Katsuya Ishizaki; Kazuya Tohge

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 194 KB
• Volume: 206
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5247

✦ Synopsis

We treat the linear differential equation ) f q A z f s 0, where k P 2 is Ž .

Ž . an integer and A z is a transcendental entire function of order A . It is shown Ž . Ž . Ž . Ž . that any non-trivial solution of the equation ) satisfies f P A , where f is the exponent of convergence of the zero-sequence of f, under the condition Ž . Ž . KN r, 1rA O T r, A , r f E for a K ) 2 k and an exceptional set E of finite

Ž .. linear measure. The second order equation f Љ q e q e q Q z f s 0, Ž .

Ž . Ž . where P z , P z are non-constant polynomials and Q z is an entire function, is 1 2 also studied.