On the boundedness of solutions of difference-differential equations

On the Boundedness of Solutions of Nonlinear Differential and Difference Equations

as 23i-i lz*l +|«'t|—»0, for fixed /. Systems of the form (1.1) are of considerable interest in dynamics, and play an important role in many branches of applied mathematics. Usually the right-hand side does not involve any derivatives. In dynamics, where t represents the time, a natural problem is the determination of the behavior of the solutions for large values of the time, and this is the c...

Boundedness of Solutions to Linear Differential Equations

In the case of a linear constant coefficient differential equation, & = Ax, where x is a (complex) n-vector and A is a (complex) nXn matrix, it is well known when all solutions are bounded; namely, if all eigenvalues of A are purely imaginary and all elementary divisions of A are simple. This condition is equivalent to the Jordan normal form, / , of A being (Hermitian) skew symmetric. That is i...

Some conditions for boundedness of solutions of difference volterra equations

On meromorphic solutions of certain type of difference equations

‎We mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+P(z)f(z+c)^n=Q(z)$‎, ‎which is a supplement of previous‎ ‎results in [K‎. ‎Liu‎, ‎L. Z‎. ‎Yang and X‎. ‎L‎. ‎Liu‎, ‎Existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎Czechoslovak Math. J. 61 (2011)‎, no. 2, ‎565--576‎, and X‎. ‎G‎. ‎Qi‎...

Liouvillian Solutions of Difference-Differential Equations

For a field k with an automorphism σ and a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y ) = AY, δ(Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), σ(x) = x+ 1, ...