A Note on the Brück Conjecture

Lü, Feng

doi:10.4134/bkms.2011.48.5.951

Bulletin of the Korean Mathematical Society

2011

DOI: 10.4134/bkms.2011.48.5.951

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A Note on the Brück Conjecture

Feng Lü¹

Abstract: Abstract. In 1996, Brück studied the relation between f and f ′ if an entire function f shares one value a CM with its first derivative f ′ and posed the famous Brück conjecture. In this work, we generalize the value a in the Brück conjecture to a small function α. Meanwhile, we prove that the Brück conjecture holds for a class of meromorphic functions.

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Cited by 2 publications

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Some results about functions that share functions with their derivative of higher order

Lü

Yuan

2013

Adv Differ Equ

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In this paper, we investigate the growth of some functions that share functions with their derivative of higher order. The first main theorem is an improvement of the result obtained by Lü (Bull. Korean Math. Soc. 48: 951-957, 2011), two examples are given to show that the conclusion is sharp. The second main theorem is of estimating, more exactly, the order of an entire function sharing polynomial, which extends the related result of Lü, Xu and Chen (Arch. Math. 92: 593-601, 2009). MSC: 30D35; 30D45

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Some results about functions that share functions with their derivative of higher order

Lü

Yuan

2013

Adv Differ Equ

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On the Transcendental Entire Solutions of a Class of Differential Equations

Lü¹,

Li²,

Yang³

2014

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we consider the differential equationwhere Q 1 and Q 2 are polynomials with Q 1 Q 2 ≡ 0, R is a rational function and α is an entire function. We consider solutions of the form F = f n , where f is an entire function and n ≥ 2 is an integer, and we prove that if f is a transcendental entire function, thenis a polynomial andf. This theorem improves some known results and answers an open question raised in [16].

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A Note on the Brück Conjecture

Cited by 2 publications

References 11 publications

Some results about functions that share functions with their derivative of higher order

Some results about functions that share functions with their derivative of higher order

On the Transcendental Entire Solutions of a Class of Differential Equations

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