Variational Methods for Fundamental Nonlinear Problems of Partial and Ordinary Differential Equations.

摘要

Substantial results documented in ten research papers were obtained under the grant. The principal achievements center about the discovery of new methods in the calculus of variations and the application of these methods to specific problems in nonlinear elliptic partial differential equations,differential geometry,nonlinear elasticity and fluid mechanics. Significant applications were the following: a complete study of large vortex rings in an ideal fluid, a vigorous variational method for the study of large deformation equilibrium states in nonlinear elasticity under general bending and buckling body forces,new results in bifurcation theory using the Morse type numbers, a new result on the simplest metrics on complex manifolds,new solvability criteria for nonlinear gradient operator equations,and an entirely new method for the study of nonlinear operator equations and boundary value problems for partial differential equations with far reaching consequences both for numerical analysis and theoretical research. (Author)