Existence of positive solutions of a fourth-order boundary value problem

被引：59
|
作者：
Ma, RY [1 ]
机构：
[1] NW Normal Univ, Dept Math, Lanzhou 730070, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2005年 / 168卷 / 02期
基金：
中国国家自然科学基金;
关键词：
existence results; eigenvalues; bifurcation methods; positive solutions;
D O I：
10.1016/j.amc.2004.10.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the fourth-order boundary value problem u'''' = f(t,u,u"), 0 < t < 1 u(0) = u(1) = u"(0) = u"(1) = 0 where f(t,u,p) = au - b p + o(vertical bar(u,p)vertical bar) near (0, 0), and f(t,u,p) = cu - dp + o(vertical bar(u,p)vertical bar) near infinity. We give conditions on the constants a, b, c, d that guarantee the existence of positive solutions. The proof of our main result is based upon global bifurcation techniques. (c) 2004 Elsevier Inc. All rights reserved.
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页码：1219 / 1231
页数：13
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