Mixed Triple Optimal Control Vector Problem for Nonlinear Triple Elliptic System

This paper studies the mixed triple optimal control vector problem (MTOCVP) controlled by nonlinear system of triple elliptic PDEs (or for short TNES) under appropriate hypotheses. The existence theorem of a unique triple state vector solution (TSVS) for the weak formulation resulting from the TNES is demonstrated by employing the Browder theorem, with fixed mixed triple control vector (MTCV). The Lipshcitz operator between the MTCV and its conforming TSVS is demonstrated continuous. The existence theorem of a mixed triple optimal control vector (MTOCV) controlling by the TNES is stated and demonstrated, under suitable assumptions.