Recent developments in nonlinear analysis

CONTENTS......Page 8
Preface......Page 6
1. Introduction......Page 12
2. The path spaces, the nearly symmetric......Page 13
The nearly symmetric......Page 15
3. M/v......Page 17
3.1. ^c and the fundamental domain......Page 18
3.2. How O1 dominates O3: A special case......Page 19
3.4. Outline of the construction of M/v......Page 21
4. The functional......Page 22
4.1. Proposition 4.1......Page 23
4.2. M*/v and the symmetric  s......Page 24
4.4. Three additional observations......Page 25
References......Page 26
1. Introduction......Page 28
2. Preliminaries......Page 29
3. Main result......Page 31
4. Concluding remarks......Page 37
References......Page 40
1. Introduction......Page 41
2. Main results......Page 42
References......Page 53
1. Introduction......Page 54
2.1. Functional framework......Page 55
2.2. Definitions......Page 56
2.3. Auxiliary lemmas......Page 57
3. Main results......Page 59
References......Page 63
1. Introduction......Page 65
2. Preliminaries......Page 66
3. Linear nonhomogeneous problem......Page 67
4. Multivalued functions......Page 71
5. Main results......Page 73
5.1. Lipschitz multivalued right-hand sides......Page 74
5.2. Upper semicontinuous right-hand sides......Page 76
5.3. Lower semicontinuous right-hand sides......Page 77
5.4. Method of lower and upper solutions......Page 78
References......Page 80
1. Introduction......Page 83
2. Necessary conditions for existence......Page 85
3. Existence in the case of natural growth and regular measure data......Page 88
3.2. Definition and main result......Page 89
3.3. Regularization and existence of approximate solutions......Page 90
3.4. A priori estimates and passage to the limit......Page 91
References......Page 97
1. Introduction......Page 99
2. Standard growth......Page 101
3. Nonstandard growth......Page 104
References......Page 110
1. Introduction......Page 112
2.1. The continuous problem......Page 113
2.2. Reformulation of the problem......Page 114
2.3. Property of stability......Page 117
2.4. The discrete problem......Page 118
3.1. The continuous problem......Page 119
3.2. The discrete problem......Page 121
3.3. Some numerical results......Page 127
Current and future developments......Page 129
References......Page 130
1. Introduction......Page 134
2. Preliminaries and basic assumptions......Page 136
3.2. Some weighted imbedding and compactness results......Page 138
3.3. Main results......Page 140
References......Page 150
1. Introduction......Page 152
2.1. Problem under consideration and basic equations......Page 154
2.2. Elastic response......Page 155
2.3. Inuence of plasticity......Page 157
3. Conclusion......Page 159
References......Page 160
1. Introduction......Page 161
2. Assumptions on the data and definition of a renormalized solution......Page 162
3. Existence result......Page 164
4. Comparison principle and uniqueness result......Page 176
References......Page 179
1. Definition and existence of renormalized solutions in Orlicz space......Page 181
2. Definition and existence of entropy solutions in Orlicz space......Page 183
3. Existence and uniqueness of solution of unilateral problems with L1-data in Orlicz spaces......Page 185
4. Existence of solutions for nonlinear elliptic degenerated equations......Page 186
4.1. Regularity and existence of weak solutions......Page 188
4.2. Existence of renormalized solutions......Page 189
References......Page 190
1. Introduction......Page 192
2. Preliminaries......Page 195
3. Main results......Page 198
4. Proof of Theorem 3.1......Page 199
5. Appendix......Page 212
References......Page 214
1. Introduction......Page 216
2. Preliminaries......Page 219
3. Proof of the main result......Page 222
References......Page 226
1. Introduction......Page 228
2. Preliminary results......Page 231
3. Existence results......Page 238
References......Page 243
1. Introduction......Page 245
2.1. Orlicz spaces......Page 247
2.2. Capacity and Bessel potentials......Page 250
3. Capacity and non linear potential in Orlicz spaces......Page 251
4.1. On the continuity of Bessel potentials in Orlicz spaces......Page 252
4.2. Instability of capacity in Orlicz spaces......Page 254
4.3. Bessel potentials in Orlicz spaces......Page 255
5.1. Maximal operators and potentials......Page 258
5.2. Quasicontinuity......Page 259
5.3. Operations on potentials, Other definition of capacity and removable singularities......Page 260
6. Capacitary type estimates in strongly nonlinear potential theory and applications......Page 261
6.2. A space of quasicontinuous functions......Page 262
6.3. Maximal operators and capacity......Page 264
7. Maximal operators, Lebesgue points and quasicontinuity in strongly nonlinear potential theory......Page 265
8. Wolff inequality in strongly nonlinear potential theory and applications......Page 266
8.1. A Wolff type inequality......Page 267
8.2. Capacity and Hausdorff measure......Page 268
9. On the A-Laplacian......Page 269
9.2. A resolvability result......Page 270
References......Page 271
1. Introduction......Page 277
2. The stochastic model for sandpile problem (cf.6)......Page 279
3. Main results......Page 281
Acknowledgements......Page 287
References......Page 288
1. Introduction......Page 289
2. Preliminaries......Page 290
3. Existence of radial solutions......Page 292
4. Zeros points of eigenfunctions......Page 294
5. Main result......Page 297
References......Page 299
1. Introduction......Page 301
2.1. Floquet approach......Page 302
2.2. Jump operators......Page 303
2.3. Resonating averages method (RAM)......Page 304
2.3.2. Second order and second order ameliorated solutions......Page 305
3.1. Forced harmonic oscillator (FHO)......Page 306
3.1.1. First order calculations......Page 307
3.1.2. Second order calculations......Page 308
3.1.3. Jump operators......Page 311
3.1.4. Comparisons and discussions......Page 313
3.2. Pulsating Harmonic Oscillator......Page 315
3.2.1. First order solutions......Page 316
3.2.2. Second order solutions......Page 318
3.3. Harmonic oscillator with a periodical frequency......Page 321
3.3.1. First order Floquet operators and Floquet states......Page 323
3.3.2. Second order Floquet operators and Floquet states......Page 325
3.4. Harmonic Oscillator with time-dependent mass and frequency......Page 329
3.4.1. First order solutions......Page 331
3.4.2. Second order solutions......Page 332
4. Conclusion......Page 336
References......Page 337
1. Introduction......Page 338
2. Preliminaries and basic assumptions......Page 339
3. Main results......Page 341
References......Page 354
1. Introduction......Page 355
2. Preliminaries......Page 356
3. Main result......Page 359
3.1. Example......Page 364
References......Page 365
1. Introduction......Page 366
2. Problem formulation......Page 367
3. Fuzzy sliding mode control design......Page 368
4. Simulation results......Page 371
References......Page 372
Author Index......Page 376