In this paper, we discuss the exponent of n-order differential equations with unbounded piecewise-constant matrix, and resolve it's solution space into the direct sum of independent subspaces on the basis of it's exponent. Our results are provide important basis for stability and qualitative study.
In this paper, we give necessary and sufficient conditions for oscillation of bounded solutions of nonlinear second order difference equation △(pn△yn)+ qnf(yn-rn) = 0. Obtained results improve theorems in the literature [3,6,7].
Consider the secnod order linear differential system with periodic coefficients x=A(t)x (*) and the stability problem of its trivial solution. In this paper, there are several conditions which are given including a necessary and sufficient condition for asymptotic stability, a necessary and sufficient condition for some kind of unstability, and a sufficient condition for stability. These conditions are expressed directly by coefficients A(t) instead of eharacteristie values of the system (*). Therefore, a feasible method of judging stability of the system (*) is offered.
