Denkowski Z. An introduction to nonlinear analysis: applications / Denkowski Z., Migörski S., Papageorgiou N.S. - New York: Kluwer Academic Publishers, 2003. - xi, 823 p. - Ref.: p.797-817. - Ind.: p.89-823. - ISBN 0-306-47456-5  Место хранения:   055 | Институт динамики систем и теории управления CO РАН | Иркутск | Библиотека

Оглавление / Contents

List of Figures ............................................... vii Preface ........................................................ ix Acknowledgments .............................................. xiii 1 NONLINEAR OPERATORS AND FIXED POINTS ......................... 1 1.1 Compact Operators ....................................... 2 1.2 Measures of Noncompactness and Set-Contractions ........ 14 1.3 Monotone Operators ..................................... 31 1.4 Accretive Operators and Nonlinear Semigroups ........... 65 1.5 Nemitsky Operators ..................................... 84 1.6 The Ekeland Variational Principle ...................... 92 1.7 Fixed Points Theorems and Inequalities ................. 99 1.8 Remarks ............................................... 130 1.9 Exercises ............................................. 138 1.10 Solutions to Exercises ................................ 144 2 ORDINARY DIFFERENTIAL EQUATIONS ............................ 169 2.1 Critical Point Theory ................................. 170 2.2 Degree Theory ......................................... 189 2.3 Initial and Boundary Value Problems for ODEs .......... 214 2.4 Differential Inclusions ............................... 256 2.5 Hamiltonian Systems ................................... 270 2.6 Remarks ............................................... 284 2.7 Exercises ............................................. 290 2.8 Solutions to Exercises ................................ 294 3 PARTIAL DIFFERENTIAL EQUATIONS ............................. 313 3.1 Eigenvalue Problems and Maximum Principles ............ 314 3.2 Semilinear and Nonlinear Elliptic Problems ............ 345 3.3 Elliptic Variational Inequalities ..................... 374 3.4 Evolution Triples ..................................... 391 3.5 Evolution Equations I - Parabolic Problems ............ 404 3.6 Evolution Equations II - Hyperbolic Problems .......... 433 3.7 Г-Convergence of Functions ............................ 453 3.8 G-Convergence of Operators ............................ 473 3.9 Remarks ............................................... 490 3.10 Exercises ............................................. 496 3.11 Solutions to Exercises ................................ 506 4 OPTIMAL CONTROL AND CALCULUS OF VARIATIONS ................. 541 4.1 Existence and Relaxation .............................. 543 4.2 Sensitivity Analysis .................................. 577 4.3 Maximum Principle ..................................... 595 4.4 Hamilton-Jacobi-Belmann Equation and Viscosity Solutions ............................................. 613 4.5 Controllability and Observability ..................... 631 4.6 Calculus of Variations and Applications ............... 654 4.7 Remarks ............................................... 683 5 MATHEMATICAL ECONOMICS ..................................... 691 5.1 Equilibria in Exchange Economies ...................... 692 5.2 Multisector Optimal Growth Models: Discrete Time ...... 706 5.3 Continuous Time Models ................................ 730 5.4 Growth Models Under Uncertainity ...................... 749 5.5 Stochastic Games ...................................... 774 5.6 Remarks ............................................... 791 References .................................................... 797 Index ......................................................... 819