This paper concerns the existence and precise expression form of entire solutions to a certain type delay-differential equation. The significance our results lie in that we generalize supplement related obtained recently.

In this paper, we study the uniqueness of entire function and its differential-difference operators. We prove following result: let f be a transcendental finite order, $$\eta $$ non-zero complex number, $$n\ge 1, k\ge 0$$ two integers b distinct numbers. If $$(\Delta _{\eta }^{n}f)^{(k)}$$ share CM IM, then $$f\equiv (\Delta .