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The articles in this volume are an outgrowth of an international conference entitled Variational and Topological Methods in the Study of Nonlinear Phe nomena, held in Pisa in January-February 2000. Under the framework of the research project Differential Equations and the Calculus of Variations, the conference was organized to celebrate the 60th birthday of Antonio Marino, one of the leaders of the research group and a significant contrib utor to the mathematical activity in this area of nonlinear analysis. The volume highlights recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological meth ods. A broad range of topics is covered, including: concentration phenomena in PDEs, variational methods with applications to PDEs and physics, pe riodic solutions of ODEs, computational aspects in topological methods, and mathematical models in biology. Though well-differentiated, the topics covered are unified through a com mon perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on PDEs and ODEs. The volume is an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors are M. Clapp, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzan towicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, M. del Pino, E. Sere, E. Schwartzman, P. Sintzoff, R. Turner, and If. Willem.
List of contents
Morse Indices at Mountain Pass Orbits of Symmetric Functionals.- On Some Linear and Nonlinear Eigenvalue Problems in Relativistic Quantum Chemistry.- Convexity at Infinity and Palais-Smale Conditions. Applications to Hamiltonian Systems.- Periodic Solutions of Nonlinear Problems with Positive Oriented Periodic Coefficients.- The Conley Index and Rigorous Numerics for Attracting Periodic Orbits.- Dynamics of a Forced Oscillator having an Obstacle.- Spike Patterns in the Super-Critical Bahri-Coron Problem.- A Semilinear Elliptic Equation on N with Unbounded Coefficients.- Traveling Waves in Natural Systems.
Summary
Covers the advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods. This work features chapters on computational aspects and applications to biology. It is suitable for researchers and graduate students.
