二阶边值问题的多重正解性  

The Existence of Multiple Positive Solutions to Second Order Boundary Value Problems

作　　者：余建辉[1] 

机构地区：[1]福州大学数学系

出　　处：《福州大学学报（自然科学版）》1998年第1期6-10,共5页Journal of Fuzhou University(Natural Science Edition)

基　　金：福建省自然科学基金

摘　　要：利用不动点指数理论证出：如果非负函数ｆ（ｔ，ｕ）满足条件，（１）存在一个测度不为零的可测集ｅ［０，１］，使ｌｉｍｍｉｎ（ｆ（ｔ，ｕ）／ｕ）＝∞，ｌｉｍｍｉｎ（ｆ（ｔ，ｕ）／ｕ）＝∞；（２）存在常数Ｐ＞０，使得当０≤ｕ≤Ｐ，０≤ｔ≤１时，ｆ（ｔ，ｕ）≤（∫１０Ｇ（ｓ，ｓ）ｄｓ）－１Ｐ，则二阶两点边值问题－ｕ″＝ｆ（ｔ，ｕ）至少存在两个正解，其中Ｇ（ｔ，ｓ）是格林函数．By using the theory of the fixed point index, this paper obtains the following result. Assuming that nonegative function f(t,u) ameets the following conditions, namely: (1)there is a measurable set e  and its measure does not equal zero, so that lim u→0 + min t∈e (f(t,u)/u)=∞ , lim u→+∞ min t∈e(f(t,u)/u)=∞ ; (2)there is a P >0, so that 0≤ u≤P and 0≤ t ≤1 implies f(t,u)≤(∫ 1 0G(s,s)ds) -1 P ,then the second order two-point boundary value problem, - u″=f(t,u) has at least two positive solutions, in which G(t, s) is the green′s function.

关 键 词：可测集 锥 正解 不动点指数 二阶边值问题 

分 类 号：O175.8[理学—数学]