Variational Methods For Strongly Indefinite Problems

Variational Methods For Strongly Indefinite Problems
Author: Yanheng Ding
Publisher: World Scientific
Total Pages: 177
Release: 2007-07-30
Genre: Mathematics
ISBN: 9814474509

This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.

Topological Methods, Variational Methods and Their Applications

Topological Methods, Variational Methods and Their Applications
Author: Haim Br‚zis
Publisher: World Scientific
Total Pages: 300
Release: 2003
Genre: Mathematics
ISBN: 9812382623

ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

Topological and Variational Methods for Nonlinear Boundary Value Problems

Topological and Variational Methods for Nonlinear Boundary Value Problems
Author: Pavel Drabek
Publisher: CRC Press
Total Pages: 172
Release: 1997-04-17
Genre: Mathematics
ISBN: 9780582309210

In the rapidly developing area of nonlinear theory of differential equations, many important results have been obtained by the use of nonlinear functional analysis based on topological and variational methods. The survey papers presented in this volume represent the current state of the art in the subject. The methods outlined in this book can be used to obtain new results concerning the existence, uniqueness, multiplicity, and bifurcation of the solutions of nonlinear boundary value problems for ordinary and partial differential equations. The contributions to this volume are from well known mathematicians, and every paper contained in this book can serve both as a source of reference for researchers working in differential equations and as a starting point for those wishing to pursue research in this direction. With research reports in the field typically scattered in many papers within various journals, this book provides the reader with recent results in an accessible form.

Topological Methods, Variational Methods And Their Applications - Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis

Topological Methods, Variational Methods And Their Applications - Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis
Author: Haim Brezis
Publisher: World Scientific
Total Pages: 300
Release: 2003-03-13
Genre: Mathematics
ISBN: 9814486760

ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University.166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrödinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms

Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms
Author: John Neuberger
Publisher: American Mathematical Soc.
Total Pages: 298
Release: 2004
Genre: Mathematics
ISBN: 0821833391

This volume contains the proceedings of the conference on Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms. It presents current research in variational methods as applied to nonlinear elliptic PDE, although several articles concern nonlinear PDE that are nonvariational and/or nonelliptic. The book contains both survey and research papers discussing important open questions and offering suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.

Nonlinear Fractional Schrödinger Equations in R^N

Nonlinear Fractional Schrödinger Equations in R^N
Author: Vincenzo Ambrosio
Publisher: Springer Nature
Total Pages: 669
Release: 2021-04-19
Genre: Mathematics
ISBN: 3030602206

This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.

Index theory in nonlinear analysis

Index theory in nonlinear analysis
Author: Chungen Liu
Publisher: Springer
Total Pages: 346
Release: 2019-05-22
Genre: Mathematics
ISBN: 981137287X

This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems. It focuses on two index theories: L-index theory (index theory for Lagrangian boundary conditions) and P-index theory (index theory for P-boundary conditions). In addition, the book introduces readers to recent advances in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations.

Djairo G. de Figueiredo - Selected Papers

Djairo G. de Figueiredo - Selected Papers
Author: Djairo G. de Figueiredo
Publisher: Springer Science & Business Media
Total Pages: 733
Release: 2014-01-07
Genre: Mathematics
ISBN: 3319028561

This volume presents a collection of selected papers by the prominent Brazilian mathematician Djairo G. de Figueiredo, who has made significant contributions in the area of Differential Equations and Analysis. His work has been highly influential as a challenge and inspiration to young mathematicians as well as in development of the general area of analysis in his home country of Brazil. In addition to a large body of research covering a variety of areas including geometry of Banach spaces, monotone operators, nonlinear elliptic problems and variational methods applied to differential equations, de Figueiredo is known for his many monographs and books. Among others, this book offers a sample of the work of Djairo, as he is commonly addressed, advancing the study of superlinear elliptic problems (both scalar and system cases), including questions on critical Sobolev exponents and maximum principles for non-cooperative elliptic systems in Hamiltonian form.

Stochastic Analysis and Applications to Finance

Stochastic Analysis and Applications to Finance
Author: Tusheng Zhang
Publisher: World Scientific
Total Pages: 465
Release: 2012
Genre: Business & Economics
ISBN: 9814383570

A collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. It covers the topics ranging from Markov processes, backward stochastic differential equations, stochastic partial differential equations, and stochastic control, to risk measure and risk theory.