The existence of positive solutions for fourth-order boundary value problem u4 (t) = f (t ,u(t)), 0 ≤ t ≤ 1 , u(0) = u(1) = u″(0) = u″(1) = θ in Banach spaces E was discussed ,where f :0 ,1 × P→ Pis continuous ,and Pis the cone of positive elements in E .An existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping .%讨论了Banach空间E中的四阶边值问题 :u(4)(t) = f(t ,u(t)), 0 ≤ t ≤ 1 , u(0) = u(1) = u″(0) = u″(1) = θ正解的存在性 ,其中 f: 0 ,1 × P → P连续 ,P为E中的正元锥 .通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果 .
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