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May  2006, 15(2): 447-479. doi: 10.3934/dcds.2006.15.447

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

Elisa Calzolari 1, , Roberta Filippucci 1, and  Patrizia Pucci 1,

1. 

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

Received  April 2005 Revised  November 2005 Published  March 2006

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].
Keywords: weight functions., Ground states, p-Laplacian operator.
Mathematics Subject Classification: Primary: 35J70; Secondary: 35J6.
Citation: Elisa Calzolari, Roberta Filippucci, Patrizia Pucci. Existence of radial solutions for the $p$-Laplacian elliptic equations with weights. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 447-479. doi: 10.3934/dcds.2006.15.447
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