Electron. J. Diff. Eqns., Vol. 2005(2005), No. 139, pp. 1-15.

Existence and uniqueness of positive solutions to a quasilinear elliptic problem in $\mathbb{R}^{N}$

Dragos-Patru Covei

Abstract:
We prove the existence of a unique positive solution to the problem
$$ -\Delta _{p}u=a(x)f(u) $$
in $\mathbb{R}^{N}$, $N>2$. Our result extended previous works by Cirstea-Radulescu and Dinu, while the proofs are based on two theorems on bounded domains, due to Diaz-Saa and Goncalves-Santos.

Submitted June 8, 2005. Published December 5, 2005.
Math Subject Classifications: 35J60, 35J70.
Key Words: Quasilinear elliptic problem; uniqueness; existence; nonexistence; lower-upper solutions.

A corrigendum was posted on October 8, 2007. Some misprints are corrected and the existence of solutions is clarified. Please see the last page of this manuscript.

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Dragos-Patru Covei
Constantin Brancusi' University of Targu-Jiu
Bulevardul Republicii, nr. 1
210152 Targu-Jiu, Romania
email: dragoscovei77@yahoo.com

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