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On Positive Solutions of p-Laplacian-type Equations

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Analysis, Partial Differential Equations and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 193))

Abstract

Let Ω be a domain in ℝd, 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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel

    Yehuda Pinchover

  2. Department of Mathematics, Uppsala University, SE-751 06, Uppsala, Sweden

    Kyril Tintarev

Authors
  1. Yehuda Pinchover
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  2. Kyril Tintarev
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università della Basilicata, Viale dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Alberto Cialdea

  2. Dipartimento di Matematico “Guido Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Paolo Emilio Ricci  & Flavia Lanzara  & 

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Dedicated to Vladimir Maz’ya on the occasion of his 70th birthday

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Pinchover, Y., Tintarev, K. (2009). On Positive Solutions of p-Laplacian-type Equations. In: Cialdea, A., Ricci, P.E., Lanzara, F. (eds) Analysis, Partial Differential Equations and Applications. Operator Theory: Advances and Applications, vol 193. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9898-9_18

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