有序 Banach 空间非线性四阶边值问题的正解

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国家自然科学基金项目

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Positive solutions for nonlinear fourth order boundary value problems in ordered Banach spaces

摘要: 讨论有序Banach 空间E中非线性四阶边值问题 $\left\{\begin{array}{ll} u^{(4)}(t)=f(t,u(t),u''(t)),\qquad 0\leqslant t\leqslant 1, \\ u(0)=u(1)=u''(0)=u''(1)=\theta, \\ \end{array} \right.$ 正解的存在性, 其中\ $f:[0, 1]\times E\times E\rightarrow E$ 连续. 在较一般的非紧性测度条件与序条件下运用凝聚映射的不动点指数理论获得了该问题正解的存在性.
- 正解
Abstract: The existence of positive solutions for nonlinear fourth order boundary value problem $\left\{\begin{array}{ll} u^{(4)}(t)=f(t,u(t),u''(t)),\qquad 0\leqslant t\leqslant 1, \\ u(0)=u(1)=u''(0)=u''(1)=\theta, \\ \end{array} \right.$ in an ordered Banach space \ $E$ is discussed, where \ $f:[0, 1]\times E\times E \rightarrow E$ is continuous. Under more general conditions of noncompactness measure and semi-ordering, an existence result of positive solutions is obtained by employing the fixed point index theory of condensing mapping.
- Positive solution