Topological characteristics of extremals of variational problems
In this extensive review, the author describes methods of investigating variational problems based on the concepts of topological index, Euler characteristic and Lyusternik-Schnirelman category. These methods are used to prove a variety of necessary and sufficient conditions of optimality, to estimate the number of critical points and critical solutions and to validate approximate algorithms for the construction of solutions of variational problems. The authors show that the methods not only extend the boundaries of the applicability of the classical methods but also make essential contributions to the task of solving those classical problems for which the classical theory is inadequate. The work contains an extensive bibliography with 219 entries.
scientific article; zbMATH DE number 889755
scientific article