关键词: 奇异方程, 积分边值, 正解, 不动点定理, Banach空间

Abstract:

By constructing a special closed convex set and using the Mönch 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.

Key words: Singular equation, Integral boundary condition, Positive solution, Fixed point theorem, Banach space.