四川师范大学学报（自然科学版）2017，Vol.40Issue(6)：791-796,6.DOI:10.3969/j.issn.1001-8395.2017.06.014
一类四阶微分方程m点边值问题的正解
Positive Solutions of m-point Boundary Value Problem for One Class of Fourth-order Differential Equation
摘要
Abstract
The existence of positive solutions for the fourth-order m-point boundary value problem {u(4)(t) +h(t)f(u)"=0,u(0) =u'(0) =u"(0) =0,u"(1) =m=2∑i=1βiu"(ηi)is considered under some conditions concerning the first eigenvalue of the relevant linear operator,where ηi ∈ (0,l),0 ＜ η1 ＜ η2 ＜ …＜ηm-2 ＜ 1,βi ∈ [0,∞) with m=2∑i=1βiηi ＜ 1.The existence of positive solutions is proved by means of fixed point index theory,and an example is given to show the application of the result.关键词
四阶微分方程/m点边值问题/正解/锥/不动点指数Key words
fourth-order equation/m-point boundary value problem/positive solution/cone/fixed point index分类
数理科学引用本文复制引用
赵微..一类四阶微分方程m点边值问题的正解[J].四川师范大学学报（自然科学版）,2017,40(6):791-796,6.基金项目
黑龙江省青年科学基金(QC2009C99)和大庆市科技计划(szdfy-2015-63) （QC2009C99）
