3.10 Additional properties of Sobolev spaces -- 3.11 Nonhomogeneous Dirichlet problem for the elliptic equation -- 3.12 Comments -- Chapter 4. Weakly nonlinear systems -- 4.1 Di erentiation of operators -- 4.2 Inverse function theorem -- 4.3 Optimal control problems for weakly nonlinear systems -- 4.4 Equations with monotone operators -- 4.5 Additional results of the functional analysis -- 4.6 Nonlinear elliptic equation -- 4.7 Optimal control problems for nonlinear elliptic equations -- 4.8 Necessary conditions of optimality -- 4.9 Optimal control problems for general functionals -- 4.10 Optimal control problems for semilinear elliptic equations -- 4.11 Di erentiation of the inverse operator -- 4.12 Comments -- Chapter 5. Strongly nonlinear systems -- 5.1 Introduction -- 5.2 Absence of the di erentiability of the inverse operator -- 5.3 Extended di erentiation of operators -- 5.4 Necessary conditions of optimality for the strongly nonlinear system -- 5.5 Boundary control for Neumann problem -- 5.6 Extended di erentiability of the inverse operator -- 5.7 Comments -- Chapter 6. Coe cients optimization control problems -- 6.1 Coe cients control problem -- 6.2 Derivative with respect to a convex set -- 6.3 Optimization control problem for bilinear systems -- 6.4 Analysis of the coe cient optimization problem -- 6.5 Nonlinear system with the control at the coe cients -- 6.6 Di erentiability with respect to a convex set for abstract systems -- 6.7 Strongly nonlinear systems with the control at the coe cients -- 6.8 Comments -- Chapter 7. Systems with nonlinear control -- 7.1 Implicit function theorem -- 7.2 Optimization control problems for abstract systems -- 7.3 Weakly nonlinear control systems -- 7.4 Extended di erentiability of the implicit function -- 7.5 Strongly nonlinear control systems -- 7.6 Comments -- Part III. Evolutional systems