Abstract
In this paper, we study the transcendental meromorphic solutions of the higher order differential-difference equations
\(w(z+1)w(z-1)+a(z)\frac{w^{(k)}(z)}{w(z)}=R(z,w(z))=\frac{P(z,w(z))}{Q(z,w(z))},\)
where \(k\) is a positive integer, \(a(z)\) is a rational function, \(P(z,w(z))\) and \(Q(z,w(z))\) are polynomials with rational coefficients in \(w(z)\) . We obtain an upper bound on the degree of \(R\) , and the degrees of \(P\) and \(Q\) satisfy certain conditions. These results generalize some of the previous results by Liu and Song to higher order case. Finally, we provide some examples to illustrate that all cases occur.
