Partial Differential Equations: Proceedings of the International Conference Held in Fez

Front Matter......Page 1
Preface......Page 8
Table of Contents......Page 9
Contributors......Page 11
Chapter 1: Nonresonance for a Nonautonomous Elliptic Problem with Respect to the Conical Fucik Spectrum......Page 13
1. Introduction......Page 14
2. First curve in the conical Fucik spectrum for the Laplacien......Page 15
3. A nonresonance problem......Page 20
References......Page 23
1. Introduction......Page 25
2. The Schroedinger Equation......Page 27
2.2 Generalized Maximum principle : Gamma-positivity.......Page 28
2.3 Anti-Maximum Principle: Gamma-negativity......Page 30
2.4 Asymptotic behaviour of solutions at infinity.......Page 31
3.1 M-matrices......Page 32
3.2 Maximum Principle......Page 33
4. Gamma q-positivity of a 2 x 2 noncooperative systems......Page 38
References......Page 39
1. Introduction......Page 43
2.1 Assumptions......Page 44
3.1 Approximating scheme......Page 45
3.2 A priori estimates......Page 46
3.3 Convergence......Page 54
References......Page 55
1. Introduction......Page 57
2. Zero-Functions......Page 59
3. Nonlinear problem with weights......Page 65
3.1 Two- weights problem......Page 66
3.2 Particular case where m(t) = n(t)......Page 70
4. Asymptotic behaviour of the first curves of Sigma......Page 71
References......Page 74
1. Introduction and results.......Page 75
2. Proof of Theorem 1......Page 78
3. Proof of Theorem 2 and Theorem 3......Page 81
References......Page 83
1. Introduction......Page 84
2. The case of a single equation for the p-Lapacian......Page 85
2.1 Maximum principle......Page 86
3.1 Maximum principle......Page 87
3.2 Existence of solutions......Page 90
References......Page 94
Chapter 7:Nonresonance Conditions on the Potential for a Neumann Problem......Page 96
1. On the first eigenvalue of -Delta p.......Page 98
2. Nonresonance under Lamda 1.......Page 99
3. Nonresonance under Lamda 2.......Page 106
References......Page 112
1. Introduction......Page 114
2. The Rho-Laplacian......Page 116
References......Page 119
1. Introduction......Page 121
2. Preliminaries......Page 122
3. Compact Imbedding......Page 123
4. Some Technical Lemmas.......Page 124
5. Existence Results......Page 127
References......Page 134
1. Definition and existence of Renormalized Solutions......Page 135
2. Renormalized solutions and usual weak solutions......Page 145
References......Page 147
1. Introduction......Page 149
2. Preliminaries......Page 151
3.1 Existence result......Page 152
3.2 Nonexistence result......Page 154
References......Page 156
Chapter 12: On the Regularizing Effect of Strongly Increasing Lower Order Terms......Page 158
1 Introduction......Page 159
2. An existence result......Page 160
3. Measures data......Page 165
References......Page 169
1. Introduction......Page 171
2. Formal results via asymptotic arguments......Page 172
3. A rigorous proof of the existence of the extraordinary orbits......Page 175
References......Page 178
1. Introduction......Page 179
2. Variational structure of the problem......Page 182
3. The variational eigenvalues of (1.6)......Page 183
4. The case when lamda is not a variational eigenvalue of (1.6)......Page 184
5. The case when lamda is a variational eigenvalue......Page 186
References......Page 188
1. Introduction and result......Page 190
2.1 An embedding result......Page 194
2.3 Intermediate derivative and interpolation lemmas......Page 195
3.1 Estimates of the \\\"almost tangential\\\" derivatives......Page 196
References......Page 198
1. Introduction and notations......Page 201
2. Preliminaries......Page 202
3. Existence and first results......Page 203
4.1 Simplicity......Page 205
4.2 Isolation......Page 207
5. Variations of the weight......Page 208
References......Page 210
1. Introduction......Page 212
2. Preliminaries......Page 213
3. Compactness results:......Page 217
References......Page 225
1. Introduction......Page 227
2. Stationary Solutions......Page 228
3. Parabolic Equation: Local existence and uniqueness......Page 235
4. Asymptotic behavior......Page 240
5. References......Page 241
1. Introduction......Page 242
2. The variational formulation......Page 244
References......Page 250
1. Introduction......Page 252
2. Gradient estimate and modulus of continuity in the regular case......Page 253
3. The Laplacien estimate in the regular case......Page 256
4. Existence of a viscosity solution of (PC) and the Laplacien estimate......Page 258
References......Page 261
1. Introduction......Page 262
2. Examples of inhomogeneous problems.......Page 263
References.......Page 267
1. Introduction......Page 269
2. Variational characterization of Cm1......Page 270
3. Some properties of Cm1......Page 273
4. Another variational characterization of the first curve......Page 275
5. Monotonicity of Cm1 with respect to the weight......Page 283
References......Page 284
1. Introduction......Page 286
2. The exponential decay......Page 287
3. The time-compact-support property......Page 289
4. The semi-classical analysis......Page 291
5. The non-compact case......Page 293
References......Page 297