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This paper is concerned with local stability, oscillatory character of positive solutions to the system of the two nonlinear difference equationsxn+1=A+xn-1p/ynpandyn+1=A+yn-1p/xnp,n=0,1,…, whereA∈(0,∞),p∈[1,∞),xi∈(0,∞), andyi∈(0,∞),i=-1,0.

This paper is concerned with dynamics of the solution to the system of two second-order nonlinear difference equations () 0, i y − ∈ ∞ , i = 0, 1. Moreover, the rate of convergence of a solution that converges to the equilibrium of the system is discussed. Finally, some numerical examples are considered to show the results obtained.

In this paper, we study the existence of a second-order impulsive differential equations depending on a parameter λ. By employing a critical point theorem, the existence of at least three solutions is obtained.

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