Webb J R L
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8SQ, UK.
Philos Trans A Math Phys Eng Sci. 2021 Feb 22;379(2191):20190383. doi: 10.1098/rsta.2019.0383. Epub 2021 Jan 4.
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 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'.
我们证明了具有导数依赖非线性项的非线性二阶非局部边值问题多个正解的存在性。我们允许非线性项关于导数二次增长。通过使用最近得到的格朗沃尔型不等式，我们得到了导数范数的界。三个例子说明了部分结果。本文是主题为“微分方程和差分方程中的拓扑度和不动点理论”的一部分。
