Existence

Abstract

In this chapter we provide existence results for nonnegative solutions of the Yamabe-type equation Δu + a(x)u-b(x)uσ = 0, σ > 1 (6.1) on the complete, noncompact, manifold M. Existence is obtained by various versions of the monotone iteration scheme (see the appendix at the end of the chapter) and we consequently concentrate on the construction of (global and local) superand subsolutions for the problem.