| Preface | 5 |
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| Contents | 7 |
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| 1 Introduction | 11 |
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| 2 Mathematical Preliminaries | 21 |
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| 2.1 Basic Functional Analysis | 21 |
| 2.2 Sobolev Spaces | 38 |
| 2.3 Operators of Monotone Type | 49 |
| 2.4 First-Order Evolution Equations | 59 |
| 2.5 Nonsmooth Analysis | 73 |
| 3 Variational Equations | 91 |
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| 3.1 Semilinear Elliptic Equations | 91 |
| 3.2 Quasilinear Elliptic Equations | 103 |
| 3.3 Quasilinear Parabolic Equations | 115 |
| 3.4 Sign-Changing Solutions via Fucik Spectrum | 133 |
| 3.5 Quasilinear Elliptic Problems of Periodic Type | 144 |
| 3.6 Notes and Comments | 151 |
| 4 Multivalued Variational Equations | 153 |
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| 4.1 Motivation and Introductory Examples | 153 |
| 4.2 Inclusions with Global Growth on Clarke’s Gradient | 165 |
| 4.3 Inclusions with Local Growth on Clarke’s Gradient | 177 |
| 4.4 Application: Difference of Multifunctions | 190 |
| 4.5 Parabolic Inclusions with Local Growth | 200 |
| 4.6 An Alternative Concept of Sub-Supersolutions | 218 |
| 4.7 Notes and Comments | 219 |
| 5 Variational Inequalities | 221 |
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| 5.1 Variational Inequalities on Closed Convex Sets | 223 |
| 5.2 Variational Inequalities with Convex Functionals | 244 |
| 5.3 Evolutionary Variational Inequalities | 256 |
| 5.4 Sub-Supersolutions and Monotone Penalty Approximations | 267 |
| 5.5 Systems of Variational Inequalities | 277 |
| 5.6 Notes and Comments | 287 |
| 6 Hemivariational Inequalities | 289 |
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| 6.1 Notion of Sub-Supersolution | 291 |
| 6.2 Quasilinear Elliptic Hemivariational Inequalities | 295 |
| 6.3 Evolutionary Hemivariational Inequalities | 309 |
| 6.4 Notes and Comments | 326 |
| 7 Variational–Hemivariational Inequalities | 329 |
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| 7.1 Elliptic Variational–Hemivariational Inequalities | 329 |
| 7.2 Evolution Variational–Hemivariational Inequalities | 346 |
| 7.3 Nonsmooth Critical Point Theory | 365 |
| 7.4 A Constraint Hemivariational Inequality | 372 |
| 7.5 Eigenvalue Problem for a Variational– Hemivariational Inequality | 378 |
| 7.6 Notes and Comments | 385 |
| List of Symbols | 388 |
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| References | 390 |
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| Index | 401 |