Maximum principle for state constrained optimal control problems governed by multisolution p-Laplacian elliptic equations in the absence of convexity

Hongwei Lou, Shu Luan

Published 2019-01-09Version 1

A state constrained optimal control problem governed by a class of multisolution p-Laplacian elliptic equations is studied in this paper. Both the control domain and cost functional considered may be non-convex. Combining the multiplicity and degeneracy of the state equation with the non-convex assumptions is the main difficulty we will overcome. By transforming the initial problem to a well-posed and non degenerate problem with a point-point mixed constraint and then using Ekeland's variational principle, the Pontryagin's maximum principle for the initial problem is obtained by passing to the limits twice.