Abstract
Abstract Let Ω be a domain in ℝd, d ≥ 2, and 1 < p < ∞. Fix V ∈ L∞ loc(Ω). Consider the functional Q and its Gâteaux derivative Qʹ given by It is assumed that Q ≥ 0 on C0 ∞(Ω). In a previous paper [22] we discussed relations between the absence of weak coercivity of the functional Q on C0 ∞(Ω) and the existence of a generalized ground state. In the present paper we study further relationships between functional-analytic properties of the functional Q and properties of positive solutions of the equation Qʹ(u) = 0.
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