| 带有不定权的二阶差分系统正解的存在性 |
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| 引用本文： | 何志乾.带有不定权的二阶差分系统正解的存在性[J].烟台大学学报(自然科学与工程版),2012,25(2):86-89. |
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| 作者姓名： | 何志乾 |
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| 作者单位： | 西北师范大学数学与信息科学学院,甘肃兰州,730070 |
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| 基金项目： | 国家自然科学基金资助项目，甘肃省自然科学基金资助项目，春辉计划 |
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| 摘 要： | 运用单调迭代法和Schauder不动点定理，获得了如下非线性二阶差分系统---当λ充分小时正解的存在性．其中1，T]z：={1，2，…，T-1，T}，且a，b：1，T]z→R，f，g：0，∞）→0，∞）连续，λ〉0为参数．
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| 关 键 词： | 差分系统 正解 单调迭代 存在性 |
Existence of Positive Solutions for a Class of Second-Order Difference Systems with Indefinite Weight |
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| HE Zhi-qian.Existence of Positive Solutions for a Class of Second-Order Difference Systems with Indefinite Weight[J].Journal of Yantai University(Natural Science and Engineering edirion),2012,25(2):86-89. |
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| Authors: | HE Zhi-qian |
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| Institution: | HE Zhi-qian(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China) |
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| Abstract: | Using the method of monotone iteration and Schauder fixed-point theorem,we prove the existence of positive solutions of the nonlinear second-order difference systems -Δu2(t-1)=λa(t)f(v(t)),t∈1,T]Z,-Δv2(t-1)=λb(t)g(u(t)),t∈1,T]Z,u(0)=u(T+1)=v(0)=v(T+1)=0,for λ sufficiently small.Where 1,T]Z={1,2,…,T-1,T},and a,b:1,T]Z→R,f,g:0,∞)→0,∞)are continuous,λ>0 is a parameter. |
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| Keywords: | difference systems positive solution monotone iteration existence |
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