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Global Bifurcation in Variational Inequalities

Global Bifurcation in Variational Inequalities PDF Author: Vy Khoi Le
Publisher: Springer Science & Business Media
ISBN: 1461218209
Category : Mathematics
Languages : en
Pages : 261

Book Description
An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.

Global Bifurcation in Variational Inequalities

Global Bifurcation in Variational Inequalities PDF Author: Vy Khoi Le
Publisher: Springer Science & Business Media
ISBN: 1461218209
Category : Mathematics
Languages : en
Pages : 261

Book Description
An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.

Progress In Variational Methods - Proceedings Of The International Conference On Variational Methods

Progress In Variational Methods - Proceedings Of The International Conference On Variational Methods PDF Author: Chungen Liu
Publisher: World Scientific
ISBN: 9814462616
Category : Mathematics
Languages : en
Pages : 249

Book Description
In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.

Progress in Variational Methods

Progress in Variational Methods PDF Author: Chungen Liu
Publisher: World Scientific
ISBN: 9814327840
Category : Mathematics
Languages : en
Pages : 249

Book Description
In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.

Multi-Valued Variational Inequalities and Inclusions

Multi-Valued Variational Inequalities and Inclusions PDF Author: Siegfried Carl
Publisher: Springer Nature
ISBN: 3030651657
Category : Mathematics
Languages : en
Pages : 596

Book Description
This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces. A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool for studying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions. This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.

Global Bifurcations and Chaos

Global Bifurcations and Chaos PDF Author: Stephen Wiggins
Publisher: Springer Science & Business Media
ISBN: 1461210429
Category : Mathematics
Languages : en
Pages : 505

Book Description
Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.

Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints

Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints PDF Author: Sergiu Aizicovici
Publisher: American Mathematical Soc.
ISBN: 0821841920
Category : Mathematics
Languages : en
Pages : 84

Book Description
In this paper the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one.

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Variational and Hemivariational Inequalities - Theory, Methods and Applications PDF Author: D. Goeleven
Publisher: Springer Science & Business Media
ISBN: 1441987584
Category : Mathematics
Languages : en
Pages : 361

Book Description
This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time. Audience: The book is suitable for researchers, and for doctoral and post-doctoral courses.

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Variational and Hemivariational Inequalities - Theory, Methods and Applications PDF Author: DANIEL Goeleven
Publisher: Springer Science & Business Media
ISBN: 9781402075384
Category : Mathematics
Languages : en
Pages : 372

Book Description
This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time. Audience: The book is suitable for researchers, and for doctoral and post-doctoral courses.

Nonlinear Elliptic and Parabolic Problems

Nonlinear Elliptic and Parabolic Problems PDF Author: Michel Chipot
Publisher: Springer Science & Business Media
ISBN: 3764373857
Category : Mathematics
Languages : en
Pages : 531

Book Description
Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields PDF Author: John Guckenheimer
Publisher: Springer Science & Business Media
ISBN: 1461211409
Category : Mathematics
Languages : en
Pages : 475

Book Description
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.