We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previousâ€¦ (More)

where yâˆ‡ is nabla derivative (see [4]). Exponential decay and stability of solutions of dynamic equations on time scales were investigated in recent papers [1, 5â€“7, 11, 12] using Lyapunovâ€™s method.â€¦ (More)

We establish error estimates for first-order linear systems of equations and linear second-order dynamic equations on time scales by using calculus on a time scales [1, 4, 5] and Birkhoff-Levinsonâ€™sâ€¦ (More)

We investigate the asymptotic solutions of the planar dynamic systems and the second order equations on a time scale by using a new version of Levinsonâ€™s asymptotic theorem. In this version the errorâ€¦ (More)

We establish a new asymptotic theorem for the nth order nonautonomous dynamic equation by its transformation to the almost diagonal system and applying Levinsonâ€™s asymptotic theorem.Ourâ€¦ (More)

We prove asymptotical stability and instability theorems for 2Ã—2 system of first-order linear dynamic equations on a time scale with complexvalued functions as coefficients. To prove stabilityâ€¦ (More)

We are concerned with the asymptotic behavior of solutions of an nth order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior ofâ€¦ (More)

We derive Wimanâ€™s asymptotic formula for the number of generalized zeros of (nontrivial) solutions of a second order dynamic equation on a time scale. The proof is based on the asymptoticâ€¦ (More)

The fundamental Poissonâ€™s formula characterizes solutions of the Dirichlet problem by their averages over circles (see [7]). Many generalizations of this formula have been proven (see for example [2,â€¦ (More)

This paper is concerned with the upwind finite-difference discretization of a quasilinear singularly perturbed boundary value problem without turning points. Koptevaâ€™s a posteriori error estimate [N.â€¦ (More)