Titlebook: Geometrical Methods in Variational Problems; N. A. Bobylev,S. V. Emel’yanov,S. K. Korovin Book 1999 Springer Science+Business Media Dordre

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https://doi.org/10.1007/978-3-658-42525-8oblems, problems of the classical calculus of variations, higher-dimensional variational problems, and mathematical programming problems. Conceptually, the homotopic method is based on the following observation: if in the process of deformation of a variational problem, an extremal is uniformly isol

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Introduction to the E3-India Model,valent to it; these theories originate in the classical studies of Poincaré, Brouwer, Kronecker, Hopf, Leray, and Schauder. The apparatus of the degree theory of mapping is one of the basic tools of nonlinear analysis and its applications. Therefore, we present the auxiliary material of this chapter

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Minimization of Nonlinear Functionals,lculus of variations, optimal control theory, mathematical physics, mechanics, .. In this chapter, we present general theorems of the minimum of nonlinear functionals, which form a basis of variational methods.

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https://doi.org/10.1007/978-3-658-42525-8, the homotopic method is based on the following observation: if in the process of deformation of a variational problem, an extremal is uniformly isolated with respect to a parameter, then its property to be a point of minimum is a homotopy invariant. This chapter is devoted to the verification of this principle, which has many applications.

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