On positive solutions of p-Laplacian-type equations

الأصل · EN

Let Ω be a domain in Rᵈ, d≥ 2, and 1<p<∞. Fix V∈ Lloc∞(Ω). Consider the functional Q and its Gâteaux derivative Q′ given by Q(u):= 1/p∫Ω. (|∇ u|ᵖ+V|u|ᵖ), Q′ (u):= -∇·(|∇ u|ᵖ⁻²∇ 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.