Consider the existence of positive solutions to the fourth-order two-point boundary value problem {u(4)(t)=a(t)f(t,u(t)),t∈[0,l],u(0) =u(1) =u″(0) =u″(1)=θ where α: [0,1]→R,f: [0,1] ×E→E are continuous. Under the certain conclusions on the first eigenvalue of the relevant linear differential equation, the existence and multiplicity results of positive solutions are obtained by constructing a special cone and using the Krasnoselskii fixed point theorem of condensing mapping. By introducing a new estimation technique on non-compact measure, assumption that uniform continuity of the nonlinear term f is deleted. The obtained results are still new even if in special scalar space.%研究Banach空间中的四阶非线性常微分方程两点边值问题u(4)(t)=a(t)f(t,u(t)),t∈[0,1],u(0)=u(1)=u"(0)=u"(1)=θ,正解的存在性,其中a:[0,1]→R,f:[0,1] ×E→E连续.通过构造一个特殊的锥,在相应线性微分方程第一特征值的相关条件下,运用凝聚映射的锥拉伸与锥压缩不动点定理,获得该问题正解的存在性与多重性结果.利用新的非紧性测度估计技巧,删去了非线性项f一致连续的要求,即使在特殊的纯量空间中讨论,所得到的结果也是新的.
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