Sufficient conditions for the -th order linear differential equation are derived which guarantee that its Cauchy function , together with its derivatives , , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.
In this paper there are generalized some results on oscillatory properties of the binomial linear differential equations of order ) for perturbed iterative linear differential equations of the same order.
In this paper a number of known results on the stability and boundedness of solutions of some scalar third-order nonlinear delay differential equations are extended to some vector third-order nonlinear delay differential equations.
The paper studies the equation in two cases: (i) , (ii) . In case (i), the global asymptotic stability of the solution is studied; in case (ii), the boundedness of all solutions is proved.
The dynamics of a prey-predator system, where predator has two stages, a juvenile stage and a mature stage, is modelled by a system of three ordinary differential equations. Stability and permanence of the system are discussed. Furthermore, we consider the harvesting of prey species and obtain the maximum sustainable yield and the optimal harvesting policy.
This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability of general control systems is studied. Some results due to Clark, Latushkin, Montgomery-Smith, Randolph, Megan, Zabczyk and Przyluski are generalized....