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Existence

  • Paolo Mastrolia
  • Marco Rigoli
  • Alberto G. Setti
Chapter
  • 641 Downloads
Part of the Progress in Mathematics book series (PM, volume 302)

Abstract

In this chapter we provide existence results for nonnegative solutions of the Yamabe-type equation
$$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$
(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.

Keywords

Smooth Boundary Ricci Curvature Open Domain Complete Manifold Yamabe Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Paolo Mastrolia
    • 1
  • Marco Rigoli
    • 1
  • Alberto G. Setti
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi die MilanoMilanoItaly
  2. 2.Dipartimento di Fisica e MatematicaUniversità dell’InsubriaComoItaly

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