Peiguang Wang

OSCILLATION CRITERIA FOR A NONLINEAR HYPERBOLIC EQUATION BOUNDARY VALUE PROBLEM

Abstract In this paper, we study a class of delay hyperbolic equations boundary value problems, and obtain sufficient conditions for the oscillation of solutions of the equation (E) with two kinds of boundary conditions.

Practical ϕ0-stability of impulsive dynamic systems on time scales☆

Abstract In this work, some criteria for practical ϕ 0 -stability and strongly practical ϕ 0 -stability of impulsive dynamic systems on time scales are obtained.

Oscillation of certain second order nonlinear damped difference equations with continuous variable

In this work, a class of second order nonlinear damped difference equations with continuous variable are investigated. Some oscillatory criteria are obtained.

On ϕ0-stability of difference equations

Abstract In this work, the notions of ϕ 0 -stability of comparison systems of difference equations are discussed, and further, using the method of cone-valued Lyapunov functions, various stability results for a very general system of difference equations are obtained.

Oscillatory theorems of a class of even-order neutral equations

A class of even-order nonlinear neutral differential equations with distributed deviating arguments is studied, and oscillatory criteria for solutions of such equations are established.

Oscillation of a class of functional parabolic differential equations

Abstract This paper investigates a class of parabolic equations with distributed deviating arguments, and obtains oscillatory theorems for such equations satisfying three kinds of boundary value conditions.

Certain second-order differential inequality of neutral type

Abstract In this paper, we give some sufficient conditions that ensure second-order delay differential inequality have no eventually positive solutions. Using the properties on the inequality, we obtain some new oscillatory criteria for all solutions of certain hyperbolic partial differential equations.

Criteria on boundedness in terms of two measures for discrete systems

A new concept of boundedness, which unifies various boundedness notions and leads to other notions connecting them, is defined in terms of two measures. An attempt for discrete systems tries to offer sufficient conditions for obtaining boundedness criteria for such concepts. The employing of vector Lyapunov functions and a new comparison principle covers several known results in usual boundedness theory and, therefore, the present framework provides an additional unification.

Asymptotic properties of solutions for first-order neutral differential equations with distributed deviating arguments*

In this paper, we study a class of first-order linear neutral differential equations with distributed deviating arguments. A number of lemmas and theorems are established to describe the asymptotic properties of nonoscillatory solutions to the equations.

On ϕ0-stability of a class of singular difference equations

This paper investigates a class of singular difference equations. Using the framework of the theory of singular difference equations and cone-valued Lyapunov functions, some necessary and sufficient conditions on the ϕ0-stability of a trivial solution of singular difference equations are obtained. Finally, an example is provided to illustrate our results.MSC:39A11.