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| Author | : Youssef Jabri |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 2011-09-15 |
| Genre | : Mathematics |
| ISBN | : 9781107403338 |
Download The Mountain Pass Theorem Book in PDF, ePub and Kindle
Joussef Jabri presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. Jabri clarifies the extensions and variants of the MPT in a complete and unified way and covers standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. He also covers the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. A bibliography and detailed index are also included.
| Author | : Youssef Jabri |
| Publisher | : |
| Total Pages | : 369 |
| Release | : 2003 |
| Genre | : Critical point theory (Mathematical analysis) |
| ISBN | : 9780511071133 |
Download The Mountain Pass Theorem Book in PDF, ePub and Kindle
This book presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The coverage includes standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. But it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants.
| Author | : Youssef Jabri |
| Publisher | : Cambridge University Press |
| Total Pages | : 382 |
| Release | : 2003-09-15 |
| Genre | : Mathematics |
| ISBN | : 9780521827218 |
Download The Mountain Pass Theorem Book in PDF, ePub and Kindle
Joussef Jabri presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. Jabri clarifies the extensions and variants of the MPT in a complete and unified way and covers standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. He also covers the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. A bibliography and detailed index are also included.
| Author | : Youssef Jabri |
| Publisher | : Cambridge University Press |
| Total Pages | : 390 |
| Release | : 2003-09-15 |
| Genre | : Mathematics |
| ISBN | : 9781139440813 |
Download The Mountain Pass Theorem Book in PDF, ePub and Kindle
This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.
| Author | : Paul H. Rabinowitz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 110 |
| Release | : 1986-07-01 |
| Genre | : Mathematics |
| ISBN | : 0821807153 |
Download Minimax Methods in Critical Point Theory with Applications to Differential Equations Book in PDF, ePub and Kindle
The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
| Author | : Michel Willem |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 168 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461241464 |
Download Minimax Theorems Book in PDF, ePub and Kindle
Many boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
| Author | : Nikolaos S. Papageorgiou |
| Publisher | : Springer |
| Total Pages | : 577 |
| Release | : 2019-02-26 |
| Genre | : Mathematics |
| ISBN | : 3030034305 |
Download Nonlinear Analysis - Theory and Methods Book in PDF, ePub and Kindle
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
| Author | : Martin Schechter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 1999-07-01 |
| Genre | : Mathematics |
| ISBN | : 9780817640958 |
Download Linking Methods in Critical Point Theory Book in PDF, ePub and Kindle
As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the Trans-Canada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on ...
| Author | : Marston Morse |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 384 |
| Release | : 1934-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821810189 |
Download The Calculus of Variations in the Large Book in PDF, ePub and Kindle
Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.
| Author | : R Precup |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 221 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401599866 |
Download Methods in Nonlinear Integral Equations Book in PDF, ePub and Kindle
Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.
