Boundary value problems for generalized n-hypercomplex differential equation.

摘要

The object of this dissertation is to deal with boundary value problems for nonlinear, higher-order, complex or hypercomplex differential equations.;The first Chapter presents the background and the recent development in this field. We present questions that have not yet been solved and outline our contributions and routes in answering these questions.;The second Chapter deals with the Riemann-Hilbert and compound boundary value problems for semilinear, n-analytic, hypercomplex differential equations. The contraction mapping and Schauder fixed-point theorems are the main tools used to solve these problems.;The third Chapter deals with the Riemann-Hilbert boundary value problems for semilinear, n-harmonic, hypercomplex differential equations. The parametric extention method and the Schouder fixed point theorem are used as the primary methods.;In the fourth Chapter we at first deals with a general Riemann-Hilbert boundary value problem for a nonlinear, n-analytic, differential equation. Then we use these results to generalize the results in Chapter 2--3 to nonlinear equations.;In the final Chapter, we deal with the Riemann boundary value problem for nonlinear, n-analytic, differential equations. We especially pay attention to the estimates for decay of the solution at infinity.