Dual variational methods in critical point theory and applications

An overview The mountain pass theorem and some applications Some variants of the mountain pass theorem The saddle point theorem Some generalizations of the mountain pass theorem Applications to Hamiltonian systems Functionals with symmetries and index theorems Multiple critical points of symmetric functionals: problems with constraints Multiple critical points of symmetric functionals: the unconstrained case Pertubations from symmetry Variational methods in bifurcation theory.

Minimax methods in critical point theory with applications to differential equations

A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.

/pdf/on-the-nature-of-turbulence-51oqh4n2pn.pdf

On the nature of turbulence

Convexity conditions and existence theorems in nonlinear elasticity

https://www.ceremade.dauphine.fr/~ekeland/Articles/OnTheVariationalPrinciple.pdf

On the variational principle

Topological methods in the theory of nonlinear integral equations

Geometrical Methods of Nonlinear Analysis

One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters."

Approximate Solution of Operator Equations

Positive linear systems : the method of positive operators

Plane vector fields

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