Concerning the uniqueness and sharing values of meromorphic functions, many results about meromorphic functions that share more than or equal to two values have been obtained. In this paper, we study meromorphic functions that share only one value, and prove the following result: For
and two meromorphic functions
share the same nonzero and finite value
with the same multiplicities, then
th root of unity,
being constants. As applications, we solve some nonlinear differential equations.