Nonlinear evolution equations and optimization problems in Banach spaces.

摘要

The aim of this study is two-fold, namely to develop an existence theory for a class of nonlinear evolution equations and to find higher order optimality conditions for nonlinear programming problems in a, Banach space.;The first objective has been achieved by using the theory of differential equations governed by m-accretive operators, compactness methods and fixed-point techniques. The investigation related to the second objective has been carried out by using higher order tangential cones.;The main contributions of our work are the following. First, we improve earlier results on the existence of solutions for nonlinear nonlocal Cauchy problems in Banach spaces, both in the time-independent case and in the time-dependent case. Next, for a nonlocal problem containing a multivalued perturbation, we show the applicability of our theory to the control of a distributed parameter system. Finally, for a class of abstract programming problems, we extend previous results on second order optimality conditions to higher order ones and give several significant examples.