Transcendental entire solutions for systems of trinomial difference and differential-difference equations

This paper is mainly concerned with the characterization of finite order transcendental entire solutions of some systems of trinomial functional equations where the equations involve $k$-th order derivatives and shifts of the functions. Our results are the generalizations of recent results given by Gao, and Liu-Yang. Moreover, we also discuss the existence of transcendental entire solutions of one differential difference equation which has not been discussed earlier in the literature. To demonstrate the precision and applicability of our findings we exhibit a series of examples.