Boundary Value Problems and Periodic Solutions of Nonlinear Ordinary, Functional and Partial Differential Equations.

摘要

This report summarizes the research findings of a three year period of G.B. Gustafson and the author in the areas of ordinary and partial differential equations (linear and nonlinear theory). In particular the results obtained are concerned with properties of Green's functions and matrices defined by linear differential operators and their implication to the study of nonlinear problems, with existence theory for periodic solutions of systems of nonlinear ordinary and elliptic partial differential equations, with nonlinear boundary value problems of Dirichlet and Neumann type for elliptic partial differential equations, with properties of nonlinear diffusion equations such as the existence of maximal and minimal solutions of initial- and initial boundary value problems and connectedness properties of solution sets, and finally with abstract coincidence and fixed point theorems which lend themselves to the study of nonlinear problems for differential equations. (Author)