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.

引用

页码：639 / 652

页数：14

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