The method of upper and lower solutions for a Lidstone boundary value problem

被引：10
|
作者：
Guo, YP [1 ]
Gao, Y
机构：
[1] Hebei Univ Sci & Technol, Coll Sci, Shijiazhuang 050018, Hebei, Peoples R China
[2] Ocean Univ China, Coll Phys & Environm Oceanog, Qingdao 266003, Peoples R China
[3] Yanbei Normal Inst, Dept Math, Datong 037000, Shanxi, Peoples R China
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2005年 / 55卷 / 03期
关键词：
n-parameter eigenvalue problem; Lidstone boundary value problem; lower solution; upper solution;
D O I：
10.1007/s10587-005-0051-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we develop the monotone method in the presence of upper and lower solutions for the 2nd order Lidstone boundary value problem u((2n))(t) = f(t, u(t), u" (t),..., u((2(n-1)))(t)), 0 < t < 1, u((2i))(0) = u((2i))(1) = 0, 0 <= i <= n-1, where f : [0, 1] x R-n -> R is continuous. We obtain sufficient conditions on f to guarantee the existence of solutions between a lower solution and an upper solution for the higher order boundary value problem.
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页码：639 / 652
页数：14
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