Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

Details Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

2006-10-13

arxiv.org/abs/math/0610431v1

Mathematics

Analysis of PDEs

Scientific paper

We are concerned with singular elliptic equations of the form $-\Delta u= p(x)(g(u)+ f(u)+|\nabla u|^a)$ in $\RR^N$ ($N\geq 3$), where $p$ is a positive weight and $0< a <1$. Under the hypothesis that $f$ is a nondecreasing function with sublinear growth and $g$ is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle.

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