Nonlinear Equations: Methods, Models and Applications

ISBN-13: 9783034894340 / Angielski / Miękka / 2012 / 268 str.

Daniela Lupo; Carlo Pagani; Bernhard Ruf

Opis

A collection of research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. Classical topics of nonlinear analysis were considered, such as calculus of variations, variational inequalities, critical point theory and their use in various aspects of the study of elliptic differential equations and systems, equations of Hamilton-Jacobi, Schrodinger and Navier-Stokes, and free boundary problems. Moreover, various models were focused upon: travelling waves in supported beams and plates, vortex condensation in electroweak theory, information theory, non-geometrical optics, and Dirac-Fock models for heavy atoms.

Spis treści

A Riemann Mapping Type Theorem in Higher Dimensions, Part I: The Conformally Flat Case with Umbilic Boundary.- Computable Information Content and a Simple Application to the Study of DNA.- Bounded Positive Critical Points of Some Multiple Integrals of the Calculus of Variations.- Hilbert Type Numbers for Polynomial ODE's.- S2-type Parametric Surfaces with Prescribed Mean Curvature and Minimal Energy.- Representations of Solutions of Hamilton-Jacobi Equations.- Nonexistence of Global Solutions of Higher Order Evolution Inequalities in ?N.- Morse Index Computations for a Class of Functionals Defined in Banach Spaces.- A Global Compactness Result for Elliptic Problems with Critical Nonlinearity on Symmetric Domains.- Variational Methods for Functionals with Lack of Strict Convexity.- Some Remarks on the Semilinear Wave Equation.- Unique Continuation Principles for Some Equations of Benjamin-Ono Type.- Well-posedness Results for the Modified Zakharov-Kuznetsov Equation.- A Class of Isoinertial One Parameter Families of Selfadjoint Operators.- Traveling Waves in Nonlinearly Supported Beams and Plates.- Solitary Waves Solutions of a Nonlinear Schrödinger Equation.- Nontrivial Solutions of a Class of Quasilinear Elliptic Problems Involving Critical Exponents.- Solutions of Semilinear Problems in Symmetric Planar Domains - ODE Behavior and Uniqueness of Branches.- Solutions of an Allen-Cahn Model Equation.- Some Equations of Non-geometrical Optics.- Speakers.