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On Positive Solutions of p-Laplacian-type Equations

  • Yehuda Pinchover
  • Kyril Tintarev
Part of the Operator Theory: Advances and Applications book series (OT, volume 193)

Abstract

Let Ω be a domain in ℝ d , d ≥ 2, and 1 < p < ∞. Fix V loc (Ω). Consider the functional Q and its Gâteaux derivative Q′ given by
$$ Q(u): = \tfrac{1} {p}\int_\Omega {(|\nabla u|^p + V|u|^p )dx, Q'(u): = - \nabla \cdot (|\nabla u|^{p - 2} \nabla u) + V|u|^{p - 2} u.} $$
In this paper we discuss a few aspects of relations between functional-analytic properties of the functional Q and properties of positive solutions of the equation Q′ (u)=0.

Mathematics Subject Classification (2000)

Primary 35J60 Secondary 35J20 35J70 49R50 

Keywords

Quasilinear elliptic operator p-Laplacian ground state positive solutions comparison principle minimal growth 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Yehuda Pinchover
    • 1
  • Kyril Tintarev
    • 2
  1. 1.Department of MathematicsTechnion - Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of MathematicsUppsala UniversityUppsalaSweden

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