On the shared values of entire functions and their partial differential polynomials in C-n

Let f be a non-constant entire function in C-n and L = D-(m) + D-(m-1) + ... + D-(1) + D-(0) be a partial differential operator, where D-(f) := Sigma(\I\=j)a(I) partial derivative(f)/partial derivative(I) xi, with all the coefficients a(I) being small meromorphic functions of f. We obtain a precise necessary and sufficient condition for f to be identically equal to L(f). As a consequence, we show that f must be identically equal to L(f) if they share two distinct finite values or small meromorphic functions of f (counting multiplicities).