A NATO Advanced Study Institute on Nonlinear Functional Analysis and Its Applications was held in Hotel Villa del Mare, Maratea, It.a1y during April 22 - May 3, 1985. This volume consists of the Proceedings of the Institute. These Proceedings include the invited lectures and contributed papers given during the Institute. The papers have been refereed. The aim of these lectures was to bring together recent and up-to-date development of the subject, and to give directions for future research. The main topics covered include: degree and generalized degree theory, results related to Hamiltonian Systems, Fixed Point theory, linear and nonlinear Differential and Partial Differential Equations, Theory of Nielsen Numbers, and applications to Dynamical Systems, Bifurcation Theory, Hamiltonian Systems, Minimax Theory, Heat Equations, Pendulum Equation, Nonlinear Boundary Value Problems, and Dirichlet and Neumann problems for elliptic equations and the periodic Dirichlet problem for semilinear beam equations. I express my sincere thanks to Professors F. E. Browder, R. Conti, A. Do1d, D. E. Edmunds and J. Mawhin members of the Advisory Committee.
Table of ContentsCohomological Methods in Non-Free G-Spaces with Applications to General Borsuk-Ulam Theorems and Critical Point Theorems for invariant Functionals.- on a Theorem of Anosov on Nielsen Numbers for Nilmanifolds.- Generalized Topological Degree and Bifurcation.- Global Results on Continuation and Bifurcation for Equivariant Maps.- Existence and Multiplicity for Semi-Linear Equations by the Duality Method.- Special Problems involving Uniqueness and Multiplicity in Hyperelasticity.- An index for Hamiltonian Systems with a Natural Order Structure.- G. Darbo’s Fixed Point Principle After 30 Years.- Best Approximation and Cones in Banach Spaces.- Invariant Manifold Theorems with Applications.- Some Applications of the Leray-Schauder Alternative to Differential Equations.- Sequences of Iterates in Locally Convex Spaces.- Periodic Solutions of Hamiltonian Systems: The Case of the Singular Potential.- Oscillations Et Analyse Non Lineaire: Proprietes Des Pulsations Des Solutions Periodiques (Cycles) De Certaines Equation Differentielles Autonomes Non Lineaires. Application de la Theorie du Degre de Leray Schauder.- A Fixed Point Theorem for Two Commuting Mappings.- Nonlinear Elliptic Problems involving Critical Sobolev Exponent in the Case of Symmetrical Domains.- Periodic Solutions of Pendulum Like Third Order Differential Equations.- Double Resonance at the First and Second Eigenvalues for the Nonlinear Heat Equation.- Generalised Riemann Invariants.- Unbounded Perturbations of Forced Harmonic Oscillations at Resonance.- Minimizing the Number of Fixed Points.- Approximate Fixed Points for Mappings in Banach Spaces.- Invariantly Complemented Subspaces and Groups with Fixed Point Property.- On a Certain Difference-Differential Equation.- Limit Cycles of Certain Polynomial Systems.- Convexity Structures and Kannan Maps.- On Some Converses of Generalized Banach Contraction Principles.- Multiplicity Results for Superlinear Elliptic Equations.- A Note on Periodic Solutions of Heat Equation with a Superlinear Term.- Fixed Point Sets on Pairs of Spaces.- Fixed Point Free Deformations on Compact Polyhedra.- Minimax Principles for a Class of Lower Semicontinuous Functions and Applications to Nonlinear Boundary Value Problems.- Fixed Point Theorems and Coincidence Theorems for Upper Hemi-Continuous Mappings.- Participants.