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

Vladimir Kondratiev·Vitali Liskevich·Vitaly Moroz·Zeev Sobol
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Abstract

We study positive supersolutions to an elliptic equation $(*)$: $-Δu=c|x|^{-s}u^p$, $p,s\in\bf R$ 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 $-\infty<p<p_*$. The value of $p_*$ is determined explicitly by $s$ and the geometry of the cone.

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Vladimir Kondratiev, Vitali Liskevich, Vitaly Moroz, Zeev Sobol. 2003-07-12. A critical phenomenon for sublinear elliptic equations in cone-like domains. https://doi.org/10.1112/s0024609305004492

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