二阶m点边值问题的三个正解  

Three positive solutions for second order m-point boundary value problems

作　　者：刘树宽[1] 

机构地区：[1]济宁学院数学系,山东济宁273155

出　　处：《山东大学学报（理学版）》2012年第10期38-44,48,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10871116);山东省高校科技计划项目(J10LA55)

摘　　要：考虑二阶m点边值问题u″(t)+q(t)f(t,u)=0,0<t<1,αu(0)-βu'(0)=0,u(1)-m∑-2i=1 kiu(ξi)=0{。其中α≥0,β≥0,q在t=0和t=1允许有奇性,f可以变号。通过构造合适的算子,用Leggett-Williams不动点定理,得到了至少3个正解。The second order m-point boundary value problems {un（t）＋q（t）f（t,u）=0,0〈t〈1, αu（0）-βu′（0）=0,u（1）-m-2∑i=1kiu（ζi）=0. is studied. Where α≥0,β≥0, q is allowed to be singular at t =0 and t = 1, fis allowed to change sign. By construc- ting available operator and using the Leggett-Williams fixed point theorem, the existence of three nontrivial positive so- lutions at least is obtained.

关 键 词：M点边值问题 奇异 变号 正解 

分 类 号：O177[理学—数学]