Nonlinear Analysis and its Applications to Differential Equations, 2001 Progress in Nonlinear Differential Equations and Their Applications Series, Vol. 43

This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations.  The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed.

Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including:

* periodic solutions of systems with p-Laplacian type operators (J. Mawhin)

* bifurcation in variational inequalities (K. Schmitt)

* a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega)

* asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl)

* mechanics on Riemannian manifolds (W. Oliva)

* techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets)

A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles. 

This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.

 

An Overview of the Method of Lower and Upper Solutions for ODEs.- On the Long-time Behaviour of Solutions to the Navier-Stokes Equations of Compressible Flow.- Periodic Solutions of Systems with p-Laplacian-like Operators.- Mechanics on Riemannian Manifolds.- Twist Mappings, Invariant Curves and Periodic Differential Equations.- Variational Inequalities, Bifurcation and Applications.- Complex Dynamics in a Class of Reversible Equations.- Symmetry and Monotonicity Results for Solutions of Certain Elliptic PDEs on Manifolds.- Nielsen Number and Multiplicity Results for Multivalued Boundary Value Problems.- Bifurcation Theory and Application to Semilinear Problems near the Resonance Parameter.- Orientation and Degree for Fredholm Maps of Index Zero Between Banach Spaces.- On the Method of Upper and Lower Solutions for First Order BVPs.- Nonlinear Optimal Control Problems for Diffusive Elliptic Equations of Logistic Type.- On The Use of Time-Maps in Nonlinear Boundary Value Problems.- Some Aspects of Nonlinear Spectral Theory.- Asymmetric Nonlinear Oscillators.- Hopf Bifurcation for a Delayed Predator-Prey Model and the Effect of Diffusion.- Galerkin-Averaging Method in Infinite-Dimensional Spaces for Weakly Nonlinear Problems.- PBVPs for Ordinary Impulsive Differential Equations.- Homoclinic and Periodic Solutions for Some Classes of Second Order Differential Equations.- Global Bifurcation for Monge-Ampère Operators.- Remarks on Boundedness of Semilinear Oscillators.- The Dual Variational Method in Nonlocal Semilinear Tricomi Problems.- Symmetry Properties of Positive Solutions of Nonlinear Differential Equations Involving the p-Laplace Operator.- A Maximum Principle with Applications to the Forced Sine-Gordon Equation.- Lipschitzian Regularity Conditions for theMinimizing Trajectories of Optimal Control Problems.- Abstract Concentration Compactness and Elliptic Equations on Unbounded Domains.