On the number of positive solutions of systems of nonlinear dynamic equations on time scales

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• 作者：Hong-Rui Sun ; Wan-Tong Li
• 关键词：Time scales ; Positive solution ; Cone ; Fixed point
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2008
• 期刊代码：72_03770427
• 类别：cp
• 出版时间：15 September 2008
• 卷：219
• 期：1
• 页码：123-133
• 文件大小：180 K

摘要

In this paper we consider the following n-dimensional second-order nonlinear system on time scales

with the Sturm–Liouville boundary conditions

where u=(u₁,…,u_n), =diag[₁,…,_n], β=diag[β₁,…,β_n], γ=diag[γ₁,…,γ_n], δ=diag[δ₁,…,δ_n]. Let and . Define i₀= number of zeros in the set {f₀,f_∞} and i_∞= number of infinities in the set {f₀,f_∞}. By using fixed point index theory, we show that:

(i) if i₀=1 or 2, then there exist λ₀>0 such that the system has i₀ positive solution(s) for λ>λ₀;