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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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An Introduction to Minimax Theorems and Their Applications to Differential Equations (Paperback, Softcover reprint of hardcover 1st ed. 2001)
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An Introduction to Minimax Theorems and Their Applications to Differential Equations (Paperback, Softcover reprint of hardcover 1st ed. 2001)
Series: Nonconvex Optimization and Its Applications, 52
Expected to ship within 10 - 15 working days
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This text is meant to be an introduction to critical point theory
and its ap- plications to differential equations. It is designed
for graduate and postgrad- uate students as well as for specialists
in the fields of differential equations, variational methods and
optimization. Although related material can be the treatment here
has the following main purposes: found in other books, * To present
a survey on existing minimax theorems, * To give applications to
elliptic differential equations in bounded do- mains and periodic
second-order ordinary differential equations, * To consider the
dual variational method for problems with continuous and
discontinuous nonlinearities, * To present some elements of
critical point theory for locally Lipschitz functionals and to give
applications to fourth-order differential equa- tions with
discontinuous nonlinearities, * To study homo clinic solutions of
differential equations via the varia- tional method. The Contents
of the book consist of seven chapters, each one divided into
several sections. A bibliography is attached to the end of each
chapter. In Chapter I, we present minimization theorems and the
mountain-pass theorem of Ambrosetti-Rabinowitz and some of its
extensions. The con- cept of differentiability of mappings in
Banach spaces, the Fnkhet's and Gateaux derivatives, second-order
derivatives and general minimization the- orems, variational
principles of Ekeland [EkI] and Borwein & Preiss [BP] are
proved and relations to the minimization problem are given.
Deformation lemmata, Palais-Smale conditions and mountain-pass
theorems are consid- ered.
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