Oscillation of impulsive partial difference equations with continuous variables

This paper is devoted to a class of linear impulsive partial difference equations with continuous variables. We establish a difference inequality without impulses, and use it to obtain various sufficient conditions for the oscillation of solutions.     

A remark for “Oscillation theorems for second-order nonlinear partial difference equations”

In this remark, we shall show a counter example for the main result of the paper [S.T. Liu, Y.Q. Liu, Oscillation theorems for second-order nonlinear partial difference equations, J. Comput. Appl. Math. 132 (2001) 479-482].     

A remark on “Oscillation of nonlinear partial difference systems”

In this remark, we shall show that the main results of the paper “Oscillation of nonlinear partial difference systems” (J. Math. Anal. Appl. 277 (2003) 689-700) are wrong.     

Oscillation of delay difference equations with several delays

In this paper, we obtain some new oscillation criteria for the difference equation with several delays

     

Oscillation of some nonlinear difference equations

We investigate the oscillatory behavior of all solutions of a new class of first order nonlinear neutral difference equations. Several explicit oscillation criteria are established. Our main results are supported by illustrative examples.     

Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations

This paper considers a class of fourth order nonlinear difference equations Δ²(r _n Δ²(y _n ) + Δ²(r _n ,f(n,n _n )=0,n ∈N(n ₀) wheref(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory. Partially Supported by the National Science Foundation of China     

Comparison theorems for second order nonlinear difference equations

New oscillation results are obtained for the second order nonlinear difference equation

Δ(rnf(Δxn−1))+g(n,xn)=0,     

Oscillatory properties of certain nonlinear fractional nabla difference equations

In this paper, we investigate the oscillation of a class of nonlinear fractional nabla difference equations. Some oscillation criteria are established.     

Oscillation criteria for first-order neutral nonlinear difference equations with variable coefficients

Consider the first-order neutral nonlinear difference equation of the form

, where τ > 0, σ_i ≥ 0 (i = 1, 2,…, m) are integers, {p_n} and {q_n} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Σ_n=0^∞ q_n = ∞ or Σ_n=0^∞ nq_n Σ_j=n^∞ q_j = ∞ commonly used in the literature.     

Oscillations of nonlinear partial difference systems

This paper studies the following two-dimensional nonlinear partial difference systems

     

Oscillation of nonlinear impulsive partial difference equations with continuous variables

By employing a difference inequality without impulses, we establish several sufficient conditions for the oscillation of solutions of a class of nonlinear impulsive partial difference equations with continuous variables.     

Oscillation and non-oscillation for second-order linear difference equations

We prove new oscillation and non-oscillation theorems for the second-order linear difference equation Δ²x_n−1 + p_nx_n = 0, where is a real sequence with p_n 0. These results are extensions of earlier results of Zhang and Zhou [Comput. Math. Appl. 39 (2000) 1–7].     

Oscillation theorems for certain delay partial difference equations

In this work we obtain some new oscillation criteria for certain delay partial difference equations with continuous arguments by some new techniques.     

Unsaturated solutions for partial difference equations with forcing terms

The concept of unsaturated infinite double sequence is introduced by making use of frequency measures. Unsaturated solutions are then studied for a partial difference equation. Conditions for all solutions to be unsaturated are obtained. Since unsaturated solutions are oscillatory, our results yield oscillation criteria.     

Oscillation of the solutions of parabolic equations with nonlinear neutral terms

In the present paper the oscillatory properties of the solutions of parabolic equations with nonlinear neutral terms are investigated. Our approach is to reduce the multi-dimensional problem to a one-dimensional problem for delay differential inequalities.     

On the oscillatory properties of certain fourth order nonlinear difference equations

Some new criteria for the oscillation of fourth order nonlinear difference equations of the form