Electron. J. Diff. Equ., Vol. 2016 (2016), No. 50, pp. 1-9.

Existence of positive radial solutions for quasilinear elliptic equations and systems

Zhijun Zhang

Abstract:
Under simple conditions on f and g, we show that existence of positive radial solutions for the quasilinear elliptic equation
$$ \hbox{div}(\phi_1(|\nabla u|) \nabla u)=a(|x|)f(u) \quad x\in \mathbb{R}^N, $$
and for the system
$$\displaylines{ \hbox{div}(\phi_1(|\nabla u|) \nabla u)=a(|x|)f(v) \quad x\in \mathbb{R}^N, \cr \hbox{div}(\phi_2(|\nabla v|) \nabla v) =b(|x|)g(u)\quad x\in \mathbb{R}^N\,. }$$

Submitted November 23, 2015. Published February 17, 2016.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Quasilinear elliptic equation; radial solutions; existence.

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Zhijun Zhang
School of Mathematics and Information Science
Yantai University
Yantai 264005, Shandong, China
email: chinazjzhang2002@163.com, zhangzj@ytu.edu.cn

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