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A boundary value problem for a non-linear difference equation

Lefebvre Mario

Archives of Control Sciences

2023

Vol. 33, No. 4

829--837

A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.