Existence results for singular three point boundary value problems on time scales
Existence results for singular three point boundary value problems on time scales
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DOI：
10.1016/j.jmaa.2004.02.049
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发表时间：
2004-07
影响因子：
1.3
通讯作者：
J. J. Dacunha-J.;John M. Davis;Parmjeet K. Singh
中科院分区：
文献类型：
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作者：
J. J. Dacunha-J.;John M. Davis;Parmjeet K. Singh
我们证明了由[公式：见正文]给出的时间尺度T上的三点边值问题正解的存在性，其中p∈(0，1)∩T是固定的，f(x，y)在y=0处是奇异的，可能在x=0，y=∞处是奇异的。我们通过应用Gatica，Oliker和Waltman的不动点定理来解决关于锥体递减的映射问题。我们还证明了满足相似三点边界条件的相关动力方程y∇∇+f(x，y)=0，yΔ∇+f(x，y)=0，y∇Δ+f(x，y)=0的类似存在性结果。
We prove the existence of a positive solution for the three point boundary value problem on time scale T given by [Formula: see text] where p∈(0,1)∩ T is fixed and f(x,y) is singular at y=0 and possibly at x=0, y=∞. We do so by applying a fixed point theorem due to Gatica, Oliker, and Waltman [J. Differential Equations 79 (1989) 62] for mappings that are decreasing with respect to a cone. We also prove the analogous existence results for the related dynamic equations y∇∇+f(x,y)=0, yΔ∇+f(x,y)=0, and y∇Δ+f(x,y)=0 satisfying similar three point boundary conditions.