Partial sharing and cross sharing of entire function with its derivative

In the paper, we investigate the uniqueness problem of a power of an entire function that share one value partially with it's linear differential polynomial and obtain a result, which improves several previous results in a large scale. Also in the paper we include some applications of our main result. Moreover, we solve the question raised by Wang and Liu (Value cross-sharing of meromorphic functions, Comput. Methods Funct. Theory (2023). https://doi.org/10.1007/s40315-023-00481-9) for a special case related to value cross-sharing.