I. Dissipative operators and differential equations on Banach spaces -- 1.0. Introduction -- 1.1. Duality type functionals -- 1.2. Dissipative operators -- 1.3. Semigroups of linear operators -- 1.4. Linear differential equations on Banach spaces -- 1.5. Nonlinear differential equations on Banach spaces -- II. Lumped parameter approach of nonlinear networks with transistors -- 2.0. Introduction -- 2.1. Mathematical model -- 2.2. Dissipativity -- 2.3. DC equations -- 2.4. Dynamic behaviour -- 2.5. An example -- III. lp-solutions of countable infinite systems of equations and applications to electrical circuits -- 3.0. Introduction -- 3.1. Statement of the problem and preliminary results -- 3.2. Properties of continuous lp-solutions -- 3.3. Existence of continuous lp-solutions for the quasiautonomous case -- 3.4. Truncation errors in linear case -- 3.5. Applications to infinite circuits -- IV. Mixed-type circuits with distributed and lumped parameters as correct models for integrated structures -- 4.0. Why mixed-type circuits? -- 4.1. Examples -- 4.2. Statement of the problem -- 4.3. Existence and uniqueness for dynamic system -- 4.4. The steady state problem -- 4.5. Other qualitative results -- 4.6. Bibliographical comments -- V. Asymptotic behaviour of mixed-type circuits. Delay time predicting -- 5.0. Introduction -- 5.1. Remarks on delay time evaluation -- 5.2. Asymptotic stability. Upper bound of delay time -- 5.3. A nonlinear mixed-type circuit -- 5.4. Comments -- VI. Numerical approximation of mixed models for digital integrated circuits -- 6.0. Introduction -- 6.1. The mathematical model -- 6.2. Construction of the system of FEM-equations -- 6.2.1. Space discretization of reg-lines -- 6.2.2. FEM-equations of lines -- 6.3. FEM-equations of the model -- 6.4. Residual evaluations -- 6.5. Steady state -- 6.6. The delay time and its a-priori upper bound -- 6.7. Examples -- 6.8. Concluding remarks -- Appendix I -- List of symbols -- References.