Finite-dimensional reductions of smooth functionals (Q2711863)

This article is devoted to some topological and differential geometrical methods in variational problems of mathematical physics. Its concrete aim is the further development of theoretical and applied aspects of the method of precise finite-dimensional reductions.NEWLINENEWLINENEWLINEContents: 1. Reducing systems. 1.1 The general topics. 1.2 Nonlinear comparison of key functions. 1.3 Examples.NEWLINENEWLINENEWLINE2. General reducing schemes. 2.1 Reducing submersions and their extensions. 2.2 Conditions of existence and uniqueness of an extremal on a Banach manifold with a Riemann framing.NEWLINENEWLINENEWLINE3. Integrable two-point boundary value problems. 3.1 Integrable reducing systems. 3.2 Examples.NEWLINENEWLINENEWLINE4. Local analysis of bifurcations of extremals. 4.1 2- and 3-dimensional pleats. 4.2 Multidimensional pleats.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00012].