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Nonlinear Analysis and its Applications to Differential Equations
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.
Stability Problems
P. Habets: Stabilité asymptotique pour des problèmes de perturbations singulières.- J.K. Hale: Stability of linear systems with delays.- V. Lakshmikantham: Stability and asymptotic behaviour of solutions of differential equations in a Banach space.- P. Negrini: On a definition of total stability for continuous or discrete dynamical systems.-N. Rouche: Théorie de la stabilité dans les équations différentielles ordinaires.- E.O. Roxin: Stability and differential games.
Singular Differential and Integral Equations with Applications
In the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular pro...
Nonlinear Elliptic Partial Differential Equations
This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.
Maximum Principles for the Hill's Equation
Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,...) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included. - Evaluates classical topics in the Hill's equation that are crucial for understanding modern physical models and non-linear applications - Describes explicit and effective conditions on maximum and anti-maximum principles - Collates information from disparate sources in one self-contained volume, with extensive referencing throughout
Minutes of Proceedings of the Institution of Civil Engineers
Vols. 39-214 (1874/75-1921/22) have a section 2 containing "Other selected papers"; issued separately, 1923-35, as the institution's Selected engineering papers.
Advances in Nonlinear Dynamics
Dedicated to Professor S. Leela in recognition of her significant contribution to the field of nonlinear dynamics and differential equations, this text consists of 38 papers contributed by experts from 15 countries, together with a survey of Professor Leela's work. The first group of papers examines stability, the second process controls, and the third section contains papers on various topics, including solutions for new classes of systems of equations and boundary problems, and proofs of basic theorems. Many of the featured problems are associated with the ideas and methods proposed and developed by Professor Leela.
Eye-tracking in Interaction
This volume presents a state-of-the-art of current research on the role of eye gaze in different types of interaction, including human-human and human-computer interaction. Approaching the phenomenon from different disciplinary and methodological angles, the chapters in the volume are united through a shared technological approach, viz. the use of eye-tracking technology for measuring speakers’ and hearers’ eye gaze patterns while engaged in interaction. Envisioned as an ‘innovating reader’, the volume addresses key questions of interdisciplinary relevance (e.g. to what extent can the analysis of fine-grained eye gaze data, obtained with eye-tracking technology, inform conversation analysis, and vice versa?), positioning (e.g. what is the semiotic status of eye gaze in relation to linguistic signaling?), and methodology (e.g. can we strike a balance between experimental control and authenticity in setting up dialogue settings with eye-tracking technology?). The exploration of these and other questions contributes to the demarcation of a burgeoning research program.
Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations
The area covered by this volume represents a broad choice of some interesting research topics in the field of dynamical systems and applications of nonlinear analysis to ordinary and partial differential equations. The contributed papers, written by well known specialists, make this volume a useful tool both for the experts (who can find recent and new results) and for those who are interested in starting a research work in one of these topics (who can find some updated and carefully presented papers on the state of the art of the corresponding subject).
Delay Differential Equations and Dynamical Systems
The meeting explored current directions of research in delay differential equations and related dynamical systems and celebrated the contributions of Kenneth Cooke to this field on the occasion of his 65th birthday. The volume contains three survey papers reviewing three areas of current research and seventeen research contributions. The research articles deal with qualitative properties of solutions of delay differential equations and with bifurcation problems for such equations and other dynamical systems. A companion volume in the biomathematics series (LN in Biomathematics, Vol. 22) contains contributions on recent trends in population and mathematical biology.
