Geodesic
A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $0 less than q less than 1, p$ is a positive weight such that $\varphi(r)=\max_{|x|=r}p(x), r\geq 0$. 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.
Classification : 35J60, 35B25, 35B50, 35R05
Keywords: ground state solution, Lane-Emden-Fowler equation, convection term, maximum principle, existence, sub-solution, super-solution 
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     author = {Xue, Hongtao and Zhang, Zhijun},
     title = {A remark on ground state solutions for {Lane-Emden-Fowler} equations with a convection term},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a106/}
}
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Xue, Hongtao; Zhang, Zhijun. A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a106/