On positive solutions of minimal growth for singular p-Laplacian with potential term

dc.creatorPinchover, Yehuda
dc.creatorTintarev, Kyril
dc.date2007-07-14
dc.date.accessioned2026-07-07T08:18:27Z
dc.date.available2026-07-07T08:18:27Z
dc.descriptionLet $Ω$ be a domain in $\mathbb{R}^d$, $d\geq 2$, and $1<p<\infty$. Fix $V\in L_{\mathrm{loc}}^\infty(Ω)$. Consider the functional $Q$ and its Gâteaux derivative $Q^\prime$ given by Q(u):=\frac{1}{p}\int_Ω(|\nabla u|^p+V|u|^p)\dx, Q^\prime (u):=-\nabla\cdot(|\nabla u|^{p-2}\nabla u)+V|u|^{p-2}u. It is assumed that $Q\geq 0$ on $C_0^\infty(Ω)$. In a previous paper we discussed relations between the absence of weak coercivity of the functional $Q$ on $C_0^\infty(Ω)$ 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 $Q^\prime (u)=0$.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0707.2169
dc.identifierhttp://arxiv.org/abs/0707.2169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134439
dc.subjectAnalysis of PDEs
dc.subjectSpectral Theory
dc.subject35J20; 35J60; 35J70; 49R50
dc.titleOn positive solutions of minimal growth for singular p-Laplacian with potential term
dc.typetext

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