The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control problems from the monograph of Cesari L. [Optimization theory and applications. New York: Springer-Verlag; 1983]. Our results are obtained not only for general problems but also for typical ones, where the production function is given by either the AK function or the Cobb–Douglas one, while the utility function can be in a linear or power form. Some open questions and conjectures about the regularity of global solutions of finite horizon optimal economic growth problems are formulated in this paper.

中文翻译：

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有限时域最优经济增长问题的解存在性定理

引用Cesari L专着中最优控制问题的Filippov存在性定理，研究了有限时域最优经济增长问题解的存在性。【最优化理论与应用。纽约：施普林格出版社；1983]。我们的结果不仅适用于一般问题，也适用于典型问题，其中生产函数由 AK 函数或 Cobb-Douglas 函数给出，而效用函数可以是线性或幂形式。本文提出了一些关于有限时域最优经济增长问题的全局解的规律性的开放性问题和猜想。