摘要
利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间.
By using Krasnosel＇skii fixed point theorem and under suitable conditions, we present the existence of single and multiple positive solutions for the following boundary value problems ：{ （-1）^q＋1 u（2q＋1）（t）=λa（t）f（u（t））,0≤t≤1, u（0）=u＇（τ）=u＇＇（1）=0 u（2j＋1）（0）=u（2j＋1）（1）=0,j=1,2,…,q-1 1 where λ〉0,1/2〈r〈1,q∈N. We derive explicit interval of λ such that for any ）,in the interval, the existence of single positive solutions for λ in appropriate interval is also discussed.
出处
《数学的实践与认识》
CSCD
北大核心
2007年第6期132-141,共10页
Mathematics in Practice and Theory
基金
山西省自然科学基金(20051005)
关键词
正解
边值问题
不动点定理
锥
positive solution
boundary value problems
fixed point theorem
cone
