The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts.
- New concepts for multi-functions as the classical tangent vectors for functions- Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions - Clarifying examples, illustrations and numerous problems, completely and carefully solved- Illustrates the applications from theory into practice - Very clear and elegant style
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1. Generalities 2. Specific preliminary results
Ordinary differential equations and inclusions 3. Nagumo type viability theorems 4. Problems of invariance 5. Viability under Carathéodory conditions 6. Viability for differential inclusions 7. Applications
Part 2 Evolution equations and inclusions 8. Viability for single-valued semilinear evolutions 9. Viability for multi-valued semilinear evolutions 10. Viability for single-valued fully nonlinear evolutions 11. Viability for multi-valued fully nonlinear evolutions 12. Carathéodory perturbations of m-dissipative operators 13. Applications