Bøger i Progress in Nonlinear Differential Equations and Their Applications serien

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets.

This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves GBP3 Weak Turbulence held at Case Western Reserve University in May 1992. Work in field can be broadly divided into two areas: * The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence.

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.

Contains research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. This work considers topics of nonlinear analysis, such as calculus of variations, variational inequalities, critical point theory, equations of Hamilton-Jacobi, Schrodinger and Navier-Stokes, and free boundary problems.

This text is devoted to evolution problems which arise in the dynamics of mechanical systems involving unilateral constraints, possibly in the presence of dry friction. Collisions may be the result. Studies of the mechanical problems are undertaken and connected areas of research are reviewed.

This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction.

Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis;

Harmonic maps are solutions to a natural geometrical variational prob lem. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science.

Devoted to minimax theorems and their applications to partial differential equations, this text presents these theorems in a simple and unified way, starting from a quantitative deformation lemma. Many applications are given to problems dealing with lack of compactness.

In the study of these phenomena an important role is played by well-chosen model equations, which are often simpler than the full equations describing the physical or biological system, but still capture its essential features.

Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O.

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

Maximum principles are bedrock results in the theory of second order elliptic equations. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.

This volume presents lectures from the Danish-Swedish Analysis Seminar 1995, covering themes in mathematical physics, spanning a wide variety of topics.

The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on modern materials research.

A summary and synthesis of recent research demonstrating that variational methods can be used to successfully handle systems with singular potential, the Lagrangian systems. The classic cases of the Kepler problem and the N-body problem are used as specific examples.

The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987.