The functional type extension of Ekeland’s variational principle [7] due to Zhong [18] is logical equivalent with it.

This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some dilecate estimates of the state and adjoint processes. This result is a generalization of Zhou’s stochastic maximum principl...

The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for the scalar field that produces field equations identical to the usual Einstein field equations minimally coupled to a scalar field. In the electromagnetic an...

We introduce several new kinds of inferior and superior limits and corresponding kinds of semicontinuity of a set-valued map. Together with the known concepts of semicontinuity, they can be used to have a clearer insight of local behaviors of maps. Then we investigate all major semicontinuity properties of solution maps to a general quasivariational inclusion. Consequences are derived for sever...