We prove the existence of multiple positive solutions of nonlinear second-order nonlocal boundary value problems with nonlinear term having derivative dependence. We allow the nonlinearity to grow quadratically with respect to derivatives. We obtain a priori bounds for norms of derivatives by using a recently obtained Gronwall-type inequality. Three examples illustrate some of the results. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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具有导数相关非线性的非局部二阶边值问题

我们证明了非线性项具有导数相关性的非线性二阶非局部边值问题的多个正解的存在性。我们允许非线性相对于导数二次增长。我们通过使用最近获得的 Gronwall 型不等式获得导数范数的先验界限。三个例子说明了一些结果。本文是主题问题“微分方程和差分方程中的拓扑度和不动点理论”的一部分。