By means of a direct and constructive method based on the theory of semiglobal C solution, the local exact boundary observability is shown for nonautonomous 1-D quasilinear wave equations. The essential difference between nonautonomous wave equations and autonomous ones is also revealed.

In this paper we study two concepts of exponential stability for variational nonautonomous difference equations in Banach spaces. Characterizations of these concepts are given. The obtained results can be considered as generalizations for variational nonautonomous difference equations of some well-known theorems due to Barbashin and Datko . MSC: 34D05, 34D20, 93D20 keywords: variational differe...

We study differentiability properties in a particular case of the Palmer’s linearization Theorem, which states the existence of an homeomorphism H between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that H is a C preserving orientation diffeomorphism ar...

Abstract In this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and prey refuge. By applying the comparison theorem of differential equations constructing suitable Lyapunov function, sufficient conditions that guarantee permanence global stability system are obtained. oscillation theory equations, set extinction predator is

Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theore...