Second Order Su cient Optimality Condition for a Nonlinear Elliptic Boundary Control Problem

Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations

This paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition. The case of boundary control is studied. Pointwise constraints on the control and certain equality and set{constraints on the state are considered. Second order suucient conditions for local optimality of controls are established.

Second Order Suucient Optimality Condition for a Nonlinear Elliptic Control Problem

Solution Diierentiability for Nonlinear Parametric Control Problems

Nonlinear Parametric Control Problems Helmut Maurer Westf alische Wilhelms-Universitat M unster, Institut f ur Numerische und instrumentelle Mathematik, Einsteinstrasse 62, 4400 M unster, Federal Republic of Germany and Hans Josef Pesch Technische Universitat M unchen, Mathematisches Institut, Arcisstrasse 21, 8000 M unchen 2, Federal Republic of Germany Abstract: We consider perturbed ...

On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints

Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to in nity or zero, respectively. In particular, the strong convergence of...

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.