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Duality and perturbation methods in ...

Ghoussoub, N. (1953-)

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Duality and perturbation methods in critical point theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Duality and perturbation methods in critical point theory/ Nassif Ghoussoub.
其他題名:	Duality & Perturbation Methods in Critical Point Theory
作者:	Ghoussoub, N.
出版者:	Cambridge :Cambridge University Press, : 1993.,
面頁冊數:	xviii, 258 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Lipschitz and smooth perturbed minimization principles -- Linear and plurisubharmonic perturbed minimization principles -- The classical min-max theorem -- A strong form of the min-max principle -- Relaxed boundary conditions in the presence of a dual set -- The critical set in the mountain pass theorem -- Group actions and multplicity of critical points -- The Palais-Smale condition around a dual set -- examples -- Morse indices of min-max critical points -- the non degenerate case -- Morse indices of min-max critical points -- the degenerate case -- Morse-tye informationon Palais-Smale sequences -- Appendices.
標題:	Critical point theory (Mathematical analysis) -
電子資源:	https://doi.org/10.1017/CBO9780511551703
ISBN:	9780511551703

Duality and perturbation methods in critical point theory
Ghoussoub, N.1953-

Duality and perturbation methods in critical point theory[electronic resource] /Duality & Perturbation Methods in Critical Point TheoryNassif Ghoussoub. - Cambridge :Cambridge University Press,1993. - xviii, 258 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;107. - Cambridge tracts in mathematics ;107..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Lipschitz and smooth perturbed minimization principles -- Linear and plurisubharmonic perturbed minimization principles -- The classical min-max theorem -- A strong form of the min-max principle -- Relaxed boundary conditions in the presence of a dual set -- The critical set in the mountain pass theorem -- Group actions and multplicity of critical points -- The Palais-Smale condition around a dual set -- examples -- Morse indices of min-max critical points -- the non degenerate case -- Morse indices of min-max critical points -- the degenerate case -- Morse-tye informationon Palais-Smale sequences -- Appendices.

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.

ISBN: 9780511551703Subjects--Topical Terms:

672100
Critical point theory (Mathematical analysis)

LC Class. No.: QA614.7 / .G48 1993

Dewey Class. No.: 514.74

Duality and perturbation methods in critical point theory
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520 $a The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.
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