四川师范大学学报（自然科学版）
四川師範大學學報（自然科學版）
사천사범대학학보（자연과학판）
JOURNAL OF SICHUAN NORMAL UNIVERSITY(NATURAL SCIENCE)
2012年
4期
505-509
,共5页
差分方程%有界性%全局渐近稳定%振动性
差分方程%有界性%全跼漸近穩定%振動性
차분방정%유계성%전국점근은정%진동성
difference equation%botmdedness%global asymptotic stability%oscillation
研究下列非线性差分方程系统解的全局性质xn+1=A+xn-1/xn,yn+1=B+yn-1/xn,n=0,1,…,其中,A,B∈(1,+∞),xi∈(0,+∞),yi∈(0,+∞),i=-1,0.特别地,利用差分方程的比较原理,证明了在满足一定的条件之下,系统的每一个正解是有界的.进一步分别得到系统正平衡解的全局渐近稳定性以及正解振动的充分条件.所得结论推广了已有的相关结果.
研究下列非線性差分方程繫統解的全跼性質xn+1=A+xn-1/xn,yn+1=B+yn-1/xn,n=0,1,…,其中,A,B∈(1,+∞),xi∈(0,+∞),yi∈(0,+∞),i=-1,0.特彆地,利用差分方程的比較原理,證明瞭在滿足一定的條件之下,繫統的每一箇正解是有界的.進一步分彆得到繫統正平衡解的全跼漸近穩定性以及正解振動的充分條件.所得結論推廣瞭已有的相關結果.
연구하렬비선성차분방정계통해적전국성질xn+1=A+xn-1/xn,yn+1=B+yn-1/xn,n=0,1,…,기중,A,B∈(1,+∞),xi∈(0,+∞),yi∈(0,+∞),i=-1,0.특별지,이용차분방정적비교원리,증명료재만족일정적조건지하,계통적매일개정해시유계적.진일보분별득도계통정평형해적전국점근은정성이급정해진동적충분조건.소득결론추엄료이유적상관결과.
In this paper,we investigate the global character of a system of two nonlinear difference equations xn+1 =A+xn-1/yn yn+1 =B+yn-1/xn, n=0,1,…,whereA,B ∈ (1,+ ∞ ),xi ∈ (0,+ ∞ ),yi ∈ (0,+ ∞ ),i =- 1,0.In particular,using comparison theorem of the difference equation,we show that every solution of the system is bounded.Some sufficient conditions for the global asymptotic stability of the positive equilibrium and the oscillatory behavior of positive solution of the system are obtained respectively.The obtained results of this paper extend previously known results in A.M.Amleh,et al (J.Math.Anal.Appl.,1999,233:790-798.).
