Existence of optimal solutions for control and variational problems with recursive objectives
This paper is devoted to the study of the existence of optimal controls in some problems related to economic growth. The dynamic mechanism is described by nonlinear ordinary differential and Volterra integral equations on finite and infinite time intervals. The Lagrange-type performance index contains the discount factor. Some results by \textit{D. A. Carlson} [J. Optimization Theory Appl. 66, No. 2, 311-336 (1990; Zbl 0711.49007)] and by \textit{R. A. Becker}, \textit{J. H. Boyd} and \textit{B. Y. Sung} [J. Econ. Theory 47, No. 1, 76-100 (1989; Zbl 0679.90014)] are generalized using the well-known Cesari's technique and earlier results by the author. Some interesting examples and counterexamples to earlier results are presented.
nonlinear ordinary differential and Volterra integral equations
scientific article; zbMATH DE number 484026