Find in Library

<p/> <p>The main purpose of this paper is to present the properties of the meromorphic solutions of complex difference equations of the form <inline-formula><graphic file="1687-1847-2009-982681-i1.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2009-982681-i2.gif"/></inline-formula> is a collection of all subsets of <inline-formula><graphic file="1687-1847-2009-982681-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-982681-i4.gif"/></inline-formula> are distinct, nonzero complex numbers, <inline-formula><graphic file="1687-1847-2009-982681-i5.gif"/></inline-formula> is a transcendental meromorphic function, <inline-formula><graphic file="1687-1847-2009-982681-i6.gif"/></inline-formula>'s are small functions relative to <inline-formula><graphic file="1687-1847-2009-982681-i7.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1847-2009-982681-i8.gif"/></inline-formula> is a rational function in <inline-formula><graphic file="1687-1847-2009-982681-i9.gif"/></inline-formula> with coefficients which are small functions relative to <inline-formula><graphic file="1687-1847-2009-982681-i10.gif"/></inline-formula>.</p>