Displaying similar documents to “Growth properties of entire functions depending on a parameter”

On a kth-order differential equation

Xiao-Min Li, Cun-Chen Gao (2006)

Annales Polonici Mathematici

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We prove a theorem on the growth of a solution of a kth-order linear differential equation. From this we obtain some uniqueness theorems. Our results improve several known results. Some examples show that the results are best possible.

Entire functions uniformly bounded on balls of a Banach space

José M. Ansemil, Jerónimo López-Salazar, Socorro Ponte (2011)

Studia Mathematica

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Let X be an infinite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B₁ ⊂ X and unbounded on another given ball B₂ ⊂ X have been obtained. In this paper we consider the problem of finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection.

Entire functions that share a function with their first and second derivatives

Feng Lü, Junfeng Xu (2012)

Annales Polonici Mathematici

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Applying the normal family theory and the theory of complex differential equations, we obtain a uniqueness theorem for entire functions that share a function with their first and second derivative, which generalizes several related results of G. Jank, E. Mues & L. Volkmann (1986), C. M. Chang & M. L. Fang (2002) and I. Lahiri & G. K. Ghosh (2009).

Entire functions that share values or small functions with their derivatives

Sheng Li, Zongsheng Gao, Jilong Zhang (2012)

Annales Polonici Mathematici

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We investigate the uniqueness of entire functions sharing values or small functions with their derivatives. One of our results gives a necessary condition on the Nevanlinna deficiency of the entire function f sharing one nonzero finite value CM with its derivative f'. Some applications of this result are provided. Finally, we prove some further results on small function sharing.