On Positive Solutions of p-Laplacian-type Equations
Yehuda Pinchover, Kyril Tintarev · Birkhäuser Basel eBooks · 2009
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 $$ Q(u): = \tfrac{1} {p}\int_\Omega {(| abla u|^p + V|u|^p )dx, Q'(u): = - abla \cdot (| abla u|^{p - 2} abla u) + V|u|^{p - 2} u.} $$ 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.