This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation of the Dirichlet conditions by considering a homogeneous Dirichlet-type condition at one extreme of the interval and an integral operator on the other one. We obtain the expression of the Green’s function related to the linear part of the equation and characterize its constant sign. Such a property will be fundamental to deduce the existence of solutions of the nonlinear problem. The results hold from fixed point theory applied to related operators defined on suitable cones.

中文翻译：

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具有扰动 Dirichlet 积分边界条件的非线性微分方程

本文致力于证明由参数依赖积分给出的具有非齐次狄利克雷条件的二阶微分方程的正解的存在性。研究的问题是 Dirichlet 条件的非局部扰动，通过考虑区间一个极端的齐次 Dirichlet 类型条件和另一个极端的积分算子。我们得到与方程线性部分相关的格林函数的表达式，并表征其常数符号。这种性质对于推断非线性问题的解的存在性至关重要。结果来自适用于定义在合适锥体上的相关算子的不动点理论。