Banach空间非线性四阶奇异积分边值问题正解的存在性

Existence of Positive Solution for Nonlinear Fourth-order Singular Differential Equation with Integral Boundary Conditions in Banach Spaces

通过构造一个特殊的非空凸闭集,利用Mnch不动点定理在有关相应线性算子的第一特征值的条件下,得到了Banach空间中具有积分边值条件的四阶奇异微分方程正解的存在性.

By constructing a special closed convex set and using the Monch fixed-point theorem, the existence of positive solution for fourth-order nonlinear singular differential equations with integral boundary conditions in a Banach space is obtained under some conditions with respect to the first eigenvalue of a linear operator.