摘要
研究了一类四阶奇异边值问题u^(4)(t)=a(t)f(t,u(t),u″(t))+b(t)g(t,u(t),u″(t)),0<t<1,u(0)=u(1)=0,αu″(0)-βu″′(0)=0,γu″(1)+δu″′(1)=0正解的存在性,在f和g满足比超线性和次线性条件更广泛的极限条件下,利用锥压缩和拉伸不动点定理获得了正解的存在性结果,推广和包含了一些已知结果.
This paper is concerned with the existence of positive solutions for a class of fourth order singular boundary value problems：{u^（4）（t）=a（t）f（t,u（t）,u＇＇（t））＋b（t）g（t,u（t）,u＇＇（t））,0〈t〈1, u（0）=u（1）=0, αu＇＇（0）-βu＇＇＇（0）=0,γu＇＇（1）＋δu＇＇＇（1）=0.The existence of positive solutions is obtained by employing the fixed-point theorem of cone expansion and compression type under the condition that f and g satisfy the limit condition which is more extensive than the existing superlinear and sublinear condition. The obtained results generalize and include some known results.
出处
《系统科学与数学》
CSCD
北大核心
2008年第5期604-615,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(10771117
10471075)
高等学校博士点专项基金(20060446001)
山东省自然科学基金(Y2007A23).
关键词
奇异边值问题
锥
正解
Singular boundary value problem, cone, positive solutions.
