caa a22 4500 475741986 CHVBK 20180406123502.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1007/BF02676336 doi (NATIONALLICENCE)springer-10.1007/BF02676336 Global comparison of finite-dimensional reduction schemes in smooth variational problems [Elektronische Daten] [Yu. Sapronov, S. Tsarev] A new criterion for global smooth equivalence of a pair of key functions corresponding to a smooth functional in the calculus of variations for a given pair of finite-dimensional reduction schemes is established. The statement is presented in abstract form (we consider a functional on a Banach space with a Fredholm gradient). The main condition is the possibility to deform the reduction schemes into each other preserving the coercivity of the key functions. As a corollary, we obtain the theorem concerning global smooth equivalence of the key functions calculated by the Lyapunov-Schmidt and Morse-Bott reduction schemes in the two-point boundary value problem for a natural mechanical system of sufficiently general form. Kluwer Academic/Plenum Publishers, 2000 variational boundary value problem nationallicence finite-dimensional reduction nationallicence coercive functional nationallicence Lyapunov-Schmidt and Morse-Bott reduction schemes nationallicence Sapronov Yu Voronezh State University, USSR aut Tsarev S. Voronezh State University, USSR aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/5(2000-05-01), 631-638 0001-4346 67:5<631 2000 67 11006 https://doi.org/10.1007/BF02676336 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676336 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sapronov Yu Voronezh State University, USSR aut NATIONALLICENCE 700 1- Tsarev S. Voronezh State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/5(2000-05-01), 631-638 0001-4346 67:5<631 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer