Andrzej Granas – författare

The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non­ linear functional analysis, emphasizing developments related to the Leray­ Schauder theory. Using for the most part geometric methods, our study cen­ ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe­ matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre­ supposes some familiarity with more advanced parts of algebraic topology. The "Miscellaneous Results and Examples", given in the form of exer­ cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The "Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.

The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non­ linear functional analysis, emphasizing developments related to the Leray­ Schauder theory. Using for the most part geometric methods, our study cen­ ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe­ matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre­ supposes some familiarity with more advanced parts of algebraic topology. The "Miscellaneous Results and Examples", given in the form of exer­ cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The "Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.

The main topics covered in this text, which contains the proceedings of a NATO ASI conference held in Montreal, are: non-smooth critical point theory; second order differential equations on manifolds and forced oscillations; topological approach to differential inclusions; periodicity of singularly perturbed delay equations; existence, multiplicity and bifurcation of solutions of nonlinear boundary value problems; some applications of the topological degree to stability theory; bifurcation problems for semilinear elliptic equations; ordinary differential equations in Banach spaces; and the centre manifold technique and complex dynamics of reaction diffusion equations.

The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non­ linear functional analysis, emphasizing developments related to the Leray­ Schauder theory. Using for the most part geometric methods, our study cen­ ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe­ matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre­ supposes some familiarity with more advanced parts of algebraic topology. The "Miscellaneous Results and Examples", given in the form of exer­ cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The "Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.

The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.