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Entire and meromorphic solutions for systems of the differential difference equations

Xu Hong Yan, Li Hong, Ding Xin

Demonstratio Mathematica

2022

Vol. 55, nr 1

676--694

With the help of the Nevanlinna theory of meromorphic functions, the purpose of this article is to describe the existence and the forms of transcendental entire and meromorphic solutions for several systems of the quadratic trinomial functional equations: {f(z)2+2αf(z)g(z+c)+g(z+c)2=1,g(z)2+2αg(z)f(z+c)+f(z+c)2=1, {f(z+c)2+2αf(z+c)g'(z)+g'(z)2=1,g(z+c)2+2αg(z+c)f'(z)+f'(z)2=1, and {f(z+c)2+2αf(z+c)g′′(z)+g′′(z)2=1,g(z+c)2+2αg(z+c)f′′(z)+f′′(z)2=1. We obtain a series of results on the forms of the entire solutions with finite order for such systems, which are some improvements and generalizations of the previous theorems given by Gao et al. Moreover, we provide some examples to explain the existence and forms of solutions for such systems in each case.

Uniqueness of differential polynomials of meromorphic functions sharing a small function without counting multiplicity

Kieu-Oanh B. T., Thuy N. T. T.

Fasciculi Mathematici

2016

Nr 57

121--135

The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function without counting multiplicity. The results of this paper are extension of some problems studied by K. Boussaf et. al. in [2] and generalization of some results of S.S. Bhoosnurmath et. al. in [4].

Entire and meromorphic solutions of linear difference equations

Dyavanal R. S., Mathai M. M.

Fasciculi Mathematici

2016

Nr 56

43--59

In this paper, we shall investigate the existence of finite order entire and meromorphic solutions of linear difference equation of the form fn(z)+p(z)fn-2(z)+L(z, f)=h(z) where L(z, f) is linear difference polynomial in f(z), p(z) is non-zero polynomial and h(z) is a meromorphic function of finite order. We also consider finite order entire solution of linear difference equation of the form fn(z)+p(z)L(z, f)-r(z)eq(z) where r(z) and q(z) are polynomials.