Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 53, pp. 1-10.

Title: A remark on ground state solutions for Lane-Emden-Fowler 
       equations with a convection term

Authors: Hongtao Xue  (Yantai Univ., Shandong, China)
         Zhijun Zhang (Yantai Univ., Shandong, China)

Abstract:
 Via  a sub-supersolution  method and  a perturbation argument, we
 study the Lane-Emden-Fowler equation
 $$
 -\Delta u =p(x)[g(u)+f(u)+|\nabla u|^q]
 $$
 in $\mathbb{R} ^N$ ($N\geq3$), where $0<q<1$, $p$ is a positive
 weight such that $\int_0^\infty r\varphi(r)dr<\infty$, where
 $\varphi(r)=\max_{|x|=r}p(x)$, $r\geq 0$. Under the
 hypotheses that both $g$ and $f$ are sublinear, which  include no
 monotonicity on the functions $g(u)$,  $f(u)$, $g(u)/u$ and
 $f(u)/u$, we show the existence of ground state solutions.
  
Submitted January 6, 2007. Published April 10, 2007.
Math Subject Classifications: 35J60, 35B25, 35B50, 35R05.
Key Words: Ground state solution; Lane-Emden-Fowler equation; 
           convection term; maximum principle; existence; 
	   sub-solution; super-solution.