Global existence and boundedness for quasi-variational systems.
This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.
We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a -pseudo almost automorphic solution. The...
Oscillatory properties of the second order nonlinear equation are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.
Some global existence criteria for quaternionic Riccati equations are established. Two of them are used to prove a completely non conjugation theorem for solutions of linear systems of ordinary differential equations.
We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification is such that...