Dynamics Reported

1. Front Matter

   Pages I-VIII

   PDF

2. Limit Relative Category and Critical Point Theory

   • G. Fournier, D. Lupo, M. Ramos, M. Willem

   Pages 1-24

3. Coexistence of Infinitely Many Stable Solutions to Reaction Diffusion Systems in the Singular Limit

   • Yasumasa Nishiura

   Pages 25-103

4. Recent Advances in Regularity of Second-order Hyperbolic Mixed Problems, and Applications

   • I. Lasiecka, R. Triggiani

   Pages 104-162

DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents Limit Relative Category and Critical Point Theory G. Fournier, D. Lupo, M. Ramos, M. Willem 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Relative Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. Relative Cupiength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 6 4. Limit Relative Category . . . . . . . . . . . . . . . . . . . . . . . '" . . . . " . . . . . . . . . . . . . . . . 10 5. The Deformation Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6. Critical Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7. Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

• Critical Point
• Hyperbolic Partial Differential Equations
• Hyperbolische partielle Differentialgleichungen
• Kritischer Punkt
• Minimax-method
• Minimaxmethode
• Reaction Diffusion Equations
• Reaktions-Diffusionsgleichungen
• Topological Invariants
• Topologische Invarianten
• differential equation
• dynamics
• minimum

• Division of Applied Mathematics, Brown University, Providence, USA

  Christopher K. R. T. Jones

• Mathematics, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland

  Urs Kirchgraber

• Mathematics, Ludwig-Maximilians University, Munich, Federal Republic of Germany

  Hans-Otto Walther

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