Existence of radial solutions for the $p$-Laplacian elliptic equations with weights

Elisa Calzolari; Roberta Filippucci; Patrizia Pucci

doi:10.3934/dcds.2006.15.447

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2006, Volume 15, Issue 2: 447-479. Doi: 10.3934/dcds.2006.15.447

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Existence of radial solutions for the $p$-Laplacian elliptic equations with weights

1.
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia

Received: March 31, 2005

Revised: October 31, 2005

Published: March 2006

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Abstract

Using the definition of solution and the qualitative properties established in the recent paper [17], some existence results are obtained both for crossing radial solutions and for positive or compactly supported radial ground states in $\mathbb R^n$ of quasilinear singular or degenerate elliptic equations with weights and with non--linearities which can be possibly singular at $x=0$ and $u=0$, respectively. The technique used is based on the papers [1] and [12]. Furthermore we obtain a non--existence theorem for radial ground states using a technique of Ni and Serrin [13].

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Mathematics Subject Classification: Primary: 35J70; Secondary: 35J60.

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