On positive solutions of minimal growth for singular p-Laplacian with potential term
| dc.creator | Pinchover, Yehuda | |
| dc.creator | Tintarev, Kyril | |
| dc.date | 2007-07-14 | |
| dc.date.accessioned | 2026-07-07T08:18:27Z | |
| dc.date.available | 2026-07-07T08:18:27Z | |
| dc.description | Let $Ω$ 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.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/0707.2169 | |
| dc.identifier | http://arxiv.org/abs/0707.2169 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134439 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 35J20; 35J60; 35J70; 49R50 | |
| dc.title | On positive solutions of minimal growth for singular p-Laplacian with potential term | |
| dc.type | text |