Value distribution of meromorphic functions concerning differences

In this paper, we study value distribution of meromorphic functions concerning differences and mainly prove the following result: Let f be a transcendental meromorphic function of 1 <=rho(f)<infinity, let c be a nonzero constant, n a positive integer, and let P, Q be two polynomials. If max{lambda(f-P),lambda(1/f)}<rho(f) and Delta(n )(c)f(sic)0, then we have (i) delta(Q,Delta(n)(c)f)=0 and lambda(Delta(n )(c)f-Q)=rho(f), for Delta P-n(c)(sic)Q; (ii) delta(Q,Delta(n)(c)f)=1 and lambda(Delta(n)(c)f-Q)<rho(f), for Delta P-n (c)equivalent to Q. The results obtained in this paper extend and improve some results due to Chen-Shon[J Math Anal Appl 2008], [Sci China Ser A 2009], Liu[Rocky Mountain J Math 2011], Cui-Yang[Acta Math Sci Ser B 2013], Chen[Complex Var Elliptic Equ 2013], Wang-Liu-Fang[Acta Math. Sinica (Chinese Ser) 2016].