On the mean values of an entire function represented by Dirichlet series
For entire functions defined by absolutely convergent Dirichlet series, a theorem on their mean values is established which include the results of Kamthan, Juneja and Awasthi.
The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation where is a difference-differential polynomial in of degree with small functions of as its coefficients, , are nonzero rational functions and , are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.