带积分边界条件的二阶非线性边值问题的正解

Positive Solutions for Second-Order Nonlinear Boundary Value Problems with Integral Boundary Conditions

摘要: 研究一类带积分边界条件的二阶非线性边值问题，通过计算给出齐次边界条件下边值问题的格林函数及性质。利用锥上的不动点定理，得到了当f满足超线性或次线性时边值问题正解的存在性结果。

Abstract: In this article, a second-order nonlinear boundary value problem with integral boundary conditions is investigated. By calculating, the Green’s function for boundary value problem subject to homogeneous boundary conditions and its properties are given. By using the fixed point theory in cones, the existence results for at least one positive solution for the problem are established when f is superlinear or sublinear.