Variational and topological methods in the study of nonlinear phenomena : [outgrowth of an international conference, held in Pisa in January - February 2000

This volume covers 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 methods. A broad range of topics is covered, including: * concentration phenomena in pdes * variational methods with applications to pdes and physics * periodic solutions of odes * computational aspects in topological methods * mathematical models in biology Though well-differentiated, the topics covered are unified through a common 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 will be an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors: M. Clapp, M. Del Pino, M. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Sere, P. Sintzoff, R. Turner , M. Willem Front Cover......Page 1 Title......Page 4 Copyright......Page 5 Contents......Page 6 Preface......Page 8 Morse Indices at Mountain Pass Orbits of Symmetric Functionals by M. Clapp......Page 10 On Some Linear and Nonlinear Eigenvalue Problems in Relativistic Quantum Chemistry by M. J. Esteban and E. Sere ......Page 24 Convexity at Infinity and Palais-Smale Conditions. Applications to Hamiltonian Systems by A. loffe and E. Schwartzman.......Page 38 Periodic Solutions of Nonlinear Problems with Positive Oriented Periodic Coefficients by W. Marzantowicz ......Page 52 The Conley Index and Rigorous Numerics for Attracting Periodic Orbits by M. Mrozek and P. Pilarczyk ......Page 74 Dynamics of a Forced Oscillator having an Obstacle by R. Ortega ......Page 84 Spike Patterns in the Super-Critical Bahri-Coron Problem by M. del Pino, P. Felmer, and M. Musso......Page 98 A Semilinear Elliptic Equation on RN with Unbounded Coefficients by P. Sintzoff and M. Willem......Page 114 Raveling Waves in Natural Systems by R.E.L.Turner......Page 124 Back Cover......Page 145 Morse indices at mountain pass orbits of symmetric functionals / M. Clapp On some linear and nonlinear Eigenvalue problems in relativistic quantum chemistry / M.J. Esteban and E. Sвerвe Convexity at infinity and Palais-Smale conditions / A. Ioffe and E. Schwartzman Periodic solutions of nonlinear problems with positive oriented periodic coefficients / W. Marzantowicz The Conley index and rigorous numerics for attracting periodic orbits / M. Mrozek and P. Pilarczyk Dynamics of a forced oscillator having an obstacle / R. Ortega Spike patterns in the super-critical Bahri-Coron problem / M. del Pino, P. Felmer, and M. Musso A semilinear elliptic equation on R[superscript]N with unbounded coefficients / P. Sintzoff and M. Willem Traveling waves in natural systems / R.E.L. Turner. This work was motivated by the problem of existence of multiple solutions of perturbed symmetric functionals.