Homotopy of Extremal Problems: Theory and Applications (de Gruyter in Nonlinear Analysis and Applications 11) (de Gruyter Nonlinear Analysis and Applications)

This monograph provides a thorough treatment of parameter-dependent extremal problems with local minimum values that remain unchanged under changes of the parameter. The authors consider the theory as well the practical treatment of those problems, both in finite-dimensional as well as in infinite-dimensional spaces. Various applications are considered, e.g., variational calculus, control theory and bifurcations theory. - Thorough treatment of parameter-dependent extremal problems with local minimum values. - Includes many applications, e.g., variational calculus, control theory and bifurcations theory. - Intended for specialists in the field of nonlinear analysis and its applications as well as for students specializing in these subjects "This volume presents the theory and some applications of the homotopy method. It begins with a full account of the required prerequisites from topology, classical functional analysis, convex and nonsmooth analysis, differential equations, and a presentation of some typical extremal problems." "Subsequently the homotopy method is described and applied to variational problems. The theory of Conley index is developed and its relation to the homotopy method is explained. Finally, a wide range of specific applications are considered."--BOOK JACKET