PageHeader : Funkcialaj Ekvacioj, 35 (1992) 321-331 Title : On the Dirichlet Problem of the Equation Title : $-\Delta u=Ku^{5}$ on the Ball in $R^{3}$ AuthorInfo : By AuthorInfo : Shigeo KAWAI AuthorInfo : (Saga University, Japan) AuthorInfo : Dedicated to Professor Noboru Tanaka on his 60th birthday section : 1. Let us consider the following equation for a given $C^{\infty}$ function $K>0$ : section : 2. In this section, we formulate the problem as a nonlinear equation on a domain of the unit sphere, and investigate the associated linear operator. section : 3. In this section, we prepare some lemmas which we use later. We assume that $K$ satisfies the assumption in Theorem throughout this section. section : References