Existence of Regular Solutions

Abstract

In view of Theorems 4.2 and 4.10 and Remarks 4.7 and 4.9, we may seek the solutions of $(\mathrm{N}^+)$ and $(\mathrm{N}^-)$ in the form of $(V\varphi )^+$ and $(V\varphi )^-$ with $\varphi \in \ 0$, that of $(\mathrm{D}^+)$ in the form of $(W\varphi )^+$ with $\varphi \in \ 1$, and that of $(\mathrm{D}^-)$ as the sum of $(W\varphi )^-$ with $\varphi \in \ 1$ and some $3\times 1$ matrix $u_0$ of the form (3.16).