Nonlinear Problems With Lack Of Compactness

Author : Giovanni Molica Bisci,Patrizia Pucci
Publisher : Walter de Gruyter GmbH & Co KG
Page : 290 pages
File Size : 43,6 Mb
Release : 2021-02-08
Category : Mathematics
ISBN : 9783110652017

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Nonlinear Problems with Lack of Compactness by Giovanni Molica Bisci,Patrizia Pucci Pdf

This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.

Author : Giovanni Molica Bisci,Patrizia Pucci
Publisher : Walter de Gruyter GmbH & Co KG
Page : 191 pages
File Size : 41,6 Mb
Release : 2021-02-08
Category : Mathematics
ISBN : 9783110648935

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Nonlinear Problems with Lack of Compactness by Giovanni Molica Bisci,Patrizia Pucci Pdf

This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.

Author : Ioan I. Vrabie
Publisher : Longman Scientific and Technical
Page : 360 pages
File Size : 54,6 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015015703047

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Compactness Methods for Nonlinear Evolutions by Ioan I. Vrabie Pdf

Author : Vicentiu D. Radulescu,Dusan D. Repovs
Publisher : CRC Press
Page : 323 pages
File Size : 41,9 Mb
Release : 2015-06-24
Category : Mathematics
ISBN : 9781498703444

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Partial Differential Equations with Variable Exponents by Vicentiu D. Radulescu,Dusan D. Repovs Pdf

Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences. The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis. The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.

Author : Thierry Cazenave,David Costa,Orlando Lopes,Raúl Manásevich,Paul Rabinowitz,Bernhard Ruf,Carlos Tomei
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 40,9 Mb
Release : 2007-08-10
Category : Mathematics
ISBN : 9783764374013

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Contributions to Nonlinear Analysis by Thierry Cazenave,David Costa,Orlando Lopes,Raúl Manásevich,Paul Rabinowitz,Bernhard Ruf,Carlos Tomei Pdf

This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t n where ? is a bounded domain of R ,n? 1, with a smooth boundary ? = ? ?? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u ?? u =?f (u)in? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.

Author : Paolo Mastrolia,Marco Rigoli,Alberto G Setti
Publisher : Birkhäuser
Page : 260 pages
File Size : 55,9 Mb
Release : 2012-08-01
Category : Mathematics
ISBN : 303480377X

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Yamabe-type Equations on Complete, Noncompact Manifolds by Paolo Mastrolia,Marco Rigoli,Alberto G Setti Pdf

The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.

Author : Michel Chipot,Pavol Quittner
Publisher : Elsevier
Page : 625 pages
File Size : 40,5 Mb
Release : 2005-08-19
Category : Mathematics
ISBN : 9780080461076

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Handbook of Differential Equations:Stationary Partial Differential Equations by Michel Chipot,Pavol Quittner Pdf

A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other. Key features: - Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field. - Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.

Author : Dajun Guo,Yeol Je Cho,Jiang Zhu
Publisher : Nova Publishers
Page : 362 pages
File Size : 52,5 Mb
Release : 2004
Category : Mathematics
ISBN : 1594540187

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Partial Ordering Methods in Nonlinear Problems by Dajun Guo,Yeol Je Cho,Jiang Zhu Pdf

Special Interest Categories: Pure and applied mathematics, physics, optimisation and control, mechanics and engineering, nonlinear programming, economics, finance, transportation and elasticity. The usual method used in studying nonlinear problems such as topological method, variational method and others are generally only suited to the nonlinear problems with continuity and compactness. However, a lots of the problems appeared in theory and applications have no continuity and compactness, For example, differential equations and integral equations in infinite dimensional spaces, various equations defined on unbounded region are generally having no compactness. The problems can been divided into three types as follows: (1) Without using compact conditions but only using some inequalities related to some ordering, the existence and uniqueness of the fixed point for increasing operators, decreasing operators and mixed monotone operators, and the convergence of the iterative sequence are obtained. Also, these results have been used to nonlinear integral equations defined on unbounded regions. (2) Without using continuity conditions but only using a very relaxed weakly compact conditions, some new fixed point theorem of increasing operators are obtained. We have applied these results to nonlinear equations with discontinuous terms. (3) They systemly use the partial ordering methods to nonlinear integro-differential equations (include impulsive type) in Banach space.

Author : Kyril Tintarev,Karl-Heinz Fieseler
Publisher : Imperial College Press
Page : 279 pages
File Size : 45,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9781860947971

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Concentration Compactness by Kyril Tintarev,Karl-Heinz Fieseler Pdf

Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.

Author : Jesús Garcia-Falset,Khalid Latrach
Publisher : Walter de Gruyter GmbH & Co KG
Page : 466 pages
File Size : 41,7 Mb
Release : 2023-03-06
Category : Mathematics
ISBN : 9783111031811

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Nonlinear Functional Analysis and Applications by Jesús Garcia-Falset,Khalid Latrach Pdf

Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.

Author : Jesús Ildefonso Díaz,David Gómez-Castro,Tatiana A. Shaposhnikova
Publisher : Walter de Gruyter GmbH & Co KG
Page : 200 pages
File Size : 53,6 Mb
Release : 2021-06-21
Category : Mathematics
ISBN : 9783110648997

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Nonlinear Reaction-Diffusion Processes for Nanocomposites by Jesús Ildefonso Díaz,David Gómez-Castro,Tatiana A. Shaposhnikova Pdf

The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.

Author : P.H. Rabinowitz,A. Ambrosetti,I. Ekeland,E.J. Zehnder
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400939332

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Periodic Solutions of Hamiltonian Systems and Related Topics by P.H. Rabinowitz,A. Ambrosetti,I. Ekeland,E.J. Zehnder Pdf

This volume contains the proceedings of a NATO Advanced Research Workshop on Periodic Solutions of Hamiltonian Systems held in II Ciocco, Italy on October 13-17, 1986. It also contains some papers that were an outgrowth of the meeting. On behalf of the members of the Organizing Committee, who are also the editors of these proceedings, I thank all those whose contributions made this volume possible and the NATO Science Committee for their generous financial support. Special thanks are due to Mrs. Sally Ross who typed all of the papers in her usual outstanding fashion. Paul H. Rabinowitz Madison, Wisconsin April 2, 1987 xi 1 PERIODIC SOLUTIONS OF SINGULAR DYNAMICAL SYSTEMS Antonio Ambrosetti Vittorio Coti Zelati Scuola Normale Superiore SISSA Piazza dei Cavalieri Strada Costiera 11 56100 Pisa, Italy 34014 Trieste, Italy ABSTRACT. The paper contains a discussion on some recent advances in the existence of periodic solutions of some second order dynamical systems with singular potentials. The aim of this paper is to discuss some recent advances in th.e existence of periodic solutions of some second order dynamical systems with singular potentials.

Author : Gershon Wolansky
Publisher : Walter de Gruyter GmbH & Co KG
Page : 224 pages
File Size : 54,5 Mb
Release : 2021-01-18
Category : Mathematics
ISBN : 9783110635485

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Optimal Transport by Gershon Wolansky Pdf

This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning.

Author : Ilya J. Bakelman
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642698811

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Convex Analysis and Nonlinear Geometric Elliptic Equations by Ilya J. Bakelman Pdf

Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.

Author : Robert Hardt
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 55,6 Mb
Release : 1996
Category : Mathematics
ISBN : 0821804316

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Nonlinear partial differential equations in differential geometry by Robert Hardt Pdf

This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.