Elsevier S & T

Handbook of Differential Equations: Stationary Partial Differential Equations: Stationary Partial Differential Equations

Chipot, Michel

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Table of contents
  • Cover
  • Contentsix
  • Prefacev
  • List of Contributorsvii
  • Contents of Previous Volumesxi
  • Contents of Volume Ixi
  • Contents of Volume IIxiii
  • Contents of Volume IIIxv
  • Contents of Volume IVxvii
  • Chapter 1. Semilinear Elliptic Systems: Existence, Multiplicity, Symmetry of Solutions1
  • 1. Introduction3
  • 2. Gradient systems5
  • 3. Hamiltonian systems7
  • 4. Nonlinearities of arbitrary growth14
  • 5. Multiplicity of solutions for elliptic systems16
  • 6. Nonvariational elliptic systems21
  • 7. Liouville theorems31
  • 8. Decay at infinite42
  • 9. Symmetry properties of the solutions43
  • 10. Some references to other questions45
  • References45
  • Chapter 2. Nonlinear Variational Problems via the Fibering Method49
  • Introduction51
  • 1. Simple examples52
  • 2. Application of bifurcation equations72
  • 3. Application to Dirichlet problems80
  • 4. Positive solutions to Neumann problems106
  • 5. Multiplicity for some quasilinear equations (Yu. Bozhkov and E. Mitidieri)159
  • 6. Multiplicity for some quasilinear systems (Yu. Bozhkov and E. Mitidieri)179
  • References207
  • Chapter 3. Superlinear Elliptic Equations and Systems211
  • 1. Introduction213
  • 2. Elliptic equations213
  • 3. The case of dimension N = 2221
  • 4. Elliptic systems, N >=3228
  • 5. Generalization to Orlicz spaces238
  • 6. A system with no growth restriction in one nonlinearity249
  • 7. A borderline case251
  • 8. Critical phenomena for the system261
  • 9. Systems in two dimensions264
  • References275
  • Chapter 4. Nonlinear Eigenvalue Problem with Quantization277
  • 1. Energy quantization279
  • 2. Mass quantization299
  • 3. Eigenvalue problem335
  • References365
  • Chapter 5. Stationary Problem of Boltzmann Equation371
  • 1. Introduction372
  • 2. Half-space problem-nonlinear boundary layer390
  • 3. Exterior problem-flow past an obstacle438
  • 4. Time-periodic solution473
  • Acknowlegements482
  • References482
  • Chapter 6. Existence and Stability of Spikes for the Gierer-Meinhardt System487
  • 1. Introduction489
  • 2. Steady states in shadow system case491
  • 3. Stability and instability in the shadow system case519
  • 4. Full Gierer-Meinhardt system: One-dimensional case542
  • 5. The full Gierer-Meinhardt system: Two-dimensional case557
  • 6. High-dimensional case: N >=3576
  • 7. Conclusions and remarks580
  • Acknowledgments581
  • References581
  • Author Index587
  • Subject Index593
Book details
  • Vendor Elsevier S & T
  • SKU 9780444532176
  • ISBN-13 9780080557311
  • Author Chipot, Michel
  • Category Mathematics
  • Subject Applied

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