Transcendental solutions of systems of complex differential-difference equations

Abstract

In this paper, by using Nevanlinna value distribution theory, complex differential theory and combining the difference equations withdifferential equations, firstly we investigate the form of transcendental entire solutions on a type of complex higher-order differential-differenceequations; some specific solutions are given. Secondly, we further consider the existence or the form of solutions on types of systems ofdifferential-difference equations; some results are obtained. Thirdly, we discuss the growth of solutions on a class of systems of complexdifferential-difference equations. Finally, we consider the characteristic functions of transcendental meromorphic solutions on a type ofcomplex $\\Delta$ difference-functional composite equations. When proper limitation of the characteristic functions on coefficients are given,the characteristic functions can be estimated; an example also shows that the condition in our theorem is precise.