Positive solutions of nonlinear three-point boundary-value problems
Positive solutions of nonlinear three-point boundary-value problems
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DOI：
10.1016/s0022-247x(02)00661-3
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发表时间：
2003-03
影响因子：
1.3
通讯作者：
Ruyun Ma;Haiyan Wang
中科院分区：
文献类型：
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作者：
Ruyun Ma;Haiyan Wang
设a∈C[0,1], b∈C([0,1],（−∞,0]）。设φ1(t)为线性边值问题的唯一解[公式：见文]我们研究了给定0<η<1和0<αφ1（η)<1的非线性边值问题的正解的存在性，h∈C（[0,1],[0,∞)）满足存在x0∈[0,1]使得h(x0)>0, f∈C([0,∞),[0,∞)）。利用锥上的不动点定理，证明了如果f是超线性或次线性，则至少存在一个正解。
Let a∈C[0,1], b∈C([0,1],(−∞,0]). Let φ1(t) be the unique solution of the linear boundary value problem [Formula: see text] We study the existence of positive solutions to the nonlinear boundary-value problem [Formula: see text] where 0<η<1 and 0<αφ1(η)<1 are given, h∈C([0,1],[0,∞)) satisfying that there exists x0∈[0,1] such that h(x0)>0, and f∈C([0,∞),[0,∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.