An Introduction to Nonlinear Analysis: Applications, Volume 2An Introduction to Nonlinear Analysis: Applications offers an exposition of the main applications of Nonlinear Analysis. Its starting point is a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. This book is an excellent springboard for anyone wishing to conduct advanced research or work on a postgraduate text. Many exercises and their solutions complement the presentation. The text is a companion to An Introduction to Nonlinear Analysis: Theory by the same authors. |
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Contents
NONLINEAR OPERATORS AND FIXED POINTS | 1 |
11 Compact Operators | 2 |
12 Measures of Noncompactness and SetContractions | 14 |
13 Monotone Operators | 31 |
14 Accretive Operators and Nonlinear Semigroups | 65 |
15 Nemitsky Operators | 84 |
16 The Ekeland Variational Principle | 92 |
17 Fixed Points Theorems and Inequalities | 99 |
35 Evolution Equations I Parabolic Problems | 404 |
36 Evolution Equations II Hyperbolic Problems | 433 |
37 rConvergence of Functions | 453 |
38 GConvergence of Operators | 473 |
39 Remarks | 490 |
310 Exercises | 496 |
311 Solutions to Exercises | 506 |
OPTIMAL CONTROL AND CALCULUS OF VARIATIONS | 541 |
18 Remarks | 130 |
19 Exercises | 138 |
110 Solutions to Exercises | 144 |
ORDINARY DIFFERENTIAL EQUATIONS | 169 |
21 Critical Point Theory | 170 |
22 Degree Theory | 189 |
23 Initial and Boundary Value Problems for ODEs | 214 |
24 Differential Inclusions | 256 |
25 Hamiltonian Systems | 270 |
26 Remarks | 284 |
27 Exercises | 290 |
28 Solutions to Exercises | 294 |
PARTIAL DIFFERENTIAL EQUATIONS | 313 |
31 Eigenvalue Problems and Maximum Principles | 314 |
32 Semilinear and Nonlinear Elliptic Problems | 345 |
33 Elliptic Variational Inequalities | 374 |
34 Evolution Triples | 391 |
41 Existence and Relaxation | 543 |
42 Sensitivity Analysis | 577 |
43 Maximum Principle | 595 |
44 HamiltonJacobiBelmann Equation and Viscosity Solutions | 613 |
45 Controllability and Observability | 631 |
46 Calculus of Variations and Applications | 654 |
47 Remarks | 683 |
MATHEMATICAL ECONOMICS | 691 |
51 Equilibria in Exchange Economies | 692 |
Discrete Time | 706 |
53 Continuous Time Models | 730 |
54 Growth Models Under Uncertainity | 749 |
55 Stochastic Games | 774 |
56 Remarks | 791 |
References | 797 |
| 819 | |
Other editions - View all
An Introduction to Nonlinear Analysis: Applications Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou No preview available - 2003 |
An Introduction to Nonlinear Analysis: Applications Zdzislaw Denkowski,Stanislaw Migórski,Nikolaos S. Papageorgiou No preview available - 2013 |
Common terms and phrases
assume B₁ bounded c₁ Cauchy problem closed coercive condition continuous contradiction convergence convex convex set Corollary defined Definition denote differential equations eigenvalue embedding exists finite dimensional fixed point function H¹(N hence Hilbert space hypothesis implies inequality integral kn+1 L¹(I L²(N Lª(I Lemma lim inf lim sup Lipschitz lower semicontinuous LP(I M₁ Math maximal monotone operator maximum principle measurable monotone operators Moreover multifunction nonempty nonlinear Note obtain optimal control point theorem Proof Proposition prove pseudomonotone recall reflexive Banach space relatively compact REMARK result S(uo satisfies Section semigroup sequence subsequence if necessary subset Suppose theory topology u₁ un(t unique solution V₁ variational vector virtue W¹º(N W¹P(N weak topology weakly compact Wpq(I xn(t