Banach空间二阶积分边值问题的正解

摘要

The existence and multiplicity of positive solutions for second order boundary value problem {- u″(t) = f(t,u(t)) ,t ∈ [o,1], au (0) - bu′(0) = ∫1o g(s)u(s) ds , cu (1) + du ′(1) = ∫10 h(s)u(s) ds are discussed. The existence and multiplicity results by using the fixed-point index theory of strict set contraction operator and doing computation of measure of noncompactness was got.%讨论了Banach空间二阶边值问题{-u"(t)=f(t,u(t)),t∈[0,1),{au(0)-bu'(0)={∫10g(s)u(s)ds,cu(1)+du'=∫10h(s)u(s)ds正解的存在性与多重性.通过对非紧性测度的计算,利用严格集压缩映射的不动点理论,给出了该问题正解存在与多个正解存在的充分条件.