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In the present paper, the maximum principle for finite horizon stateconstrained problems from the book by R. Vinter [\textit{Optimal Control},Birkh\"auser, Boston, 2000; Theorem~9.3.1] is analyzed via parametric examples.The latter has origin in a recent paper by V.~Basco, P.~Cannarsa, andH.~Frankowska, and resembles the optimal growth problem in mathematicaleconomics. The solution existence of these parametric examples is establishedby invoking Filippov's existence theorem for Mayer problems. Since the maximumprinciple is only a necessary condition for local optimal processes, a largeamount of additional investigations is needed to obtain a comprehensivesynthesis of finitely many processes suspected for being local minimizers. Ouranalysis not only helps to understand the principle in depth, but also servesas a sample of applying it to meaningful prototypes of economic optimal growthmodels. Problems with unilateral state constraints have been studied in Part 1of the paper. Problems with bilateral state constraints are addressed in thisPart 2.

Analyzing a Maximum Principle for Finite Horizon State Constrained  Problems via Parametric Examples. Part 2: Problems with Bilateral State  Constraints