Topological characteristics and the Fredholm analysis in nonlinear problems
The author presents several new results of Voronezh mathematicians. Section I contains a resume of the results by the author and O. V. Kunakovskaya. They extend a construction from the Arnold theory of boundary singularities to the infinite-dimensional case. It follows a theorem concerning problems of longitudinal acoustic waves in a crystal with a given elastic modulus tensor. Section II contains an exposition of results by Zvyagin, Sapronov, Ratiner etc. devoted to the problems of nonlinear theory of elasticity, problems of differential geometry, etc. In the last third Section a boundary value problem for the Monge-Ampère equation is formulated. Finally other applications of Fredholm theory of nonlinear mappings are enumerated.
scientific article; zbMATH DE number 795230