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一类非线性差分方程系统解的性质

, PP. 505-509

Keywords: 差分方程,有界性,全局渐近稳定,振动性

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Abstract:

研究下列非线性差分方程系统解的全局性质xn+1=A+(xn-1)/(yn),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.

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