An existence result for optimal economic growth problems

Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis

“…Necessary conditions generalising standard Pontryagin maximum principle from Aseev and Veliov [3,4] and Balder's [5] existence theorem are stated in sections "Aseev and Veliov Extension of the Pontryagin Maximum Principle" and "Existence of Optimal Solution", while we prove our model fulfils the assumptions of those theorems in sections "Checking Assumptions for Theorem 5 for the Model Described in Sect. 2" and "Checking Assumptions for Theorem 6 for the Model Described in Sect.…”

“…We use the existence theorem of Balder [5,Theorem 3.6], which we cite in a simplified form, suiting our model in which both state and control variables sets are constant, not coupled, and the initial condition is fixed.…”

An infinite-horizon maximum principle with bounds on the adjoint variable

“…R such that 6 lim t!1 oðtÞ ¼ 0 and, for any admissible pair ðx; uÞ of system (1), subject to (2) and (3), we have Z 1 T e Àrt hðx; uÞ dtpoðTÞ (5) for all T40: With this and the uniqueness of the optimal control in terms of ðx; cÞ (guaranteed by H4), Theorem 3.6 by Balder (1983) implies the existence of a solution to the infinite-horizon optimal control problem (P). 7…”

Infinite-horizon optimal advertising in a market for durable goods

“…where m :¼ maxf% u; gg: With this, Theorem 3.6 in Reference [25] guarantees the existence of a solution to the infinite-horizon optimal control problem (P). 9 …”

“…Outline: The next section will state the problem, report on the existence of an optimal solution based on Reference [25], and provide a simplifying equivalent reformulation. In Section 3, on the basis of the finite-horizon Pontryagin Maximum Principle [17], we will construct first-order necessary optimality conditions for our problem (P) that include growth conditions in the form of upper and lower exponential bounds on the adjoint variables which converge to zero as time tends towards infinity.…”