A critical phenomenon for sublinear elliptic equations in cone-like domains

Details A critical phenomenon for sublinear elliptic equations in cone-like domains A critical phenomenon for sublinear elliptic equations in cone-like domains

2003-07-12

arxiv.org/abs/math/0307183v1

Mathematics

Analysis of PDEs

6 pages, 2 figures

Scientific paper

We study positive supersolutions to an elliptic equation $(*)$: $-\Delta u=c|x|^{-s}u^p$, $p,s\in\bf R$ in cone-like domains in $\bf R^N$ ($N\ge 2$). We prove that in the sublinear case $p<1$ there exists a critical exponent $p_*<1$ such that equation $(*)$ has a positive supersolution if and only if $-\infty

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