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

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.

Keywords

• Quasilinear elliptic problem
• uniqueness
• existence
• nonexistence
• lower-upper solutions.