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Entire solutions of sublinear elliptic equations in anisotropic media

Teodora Liliana Dinu
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Abstract

We study the nonlinear elliptic problem $-Δu=ρ(x)f(u)$ in $\RR^N$ ($N\geq 3$), $\lim\_{|x|\ri\infty}u(x)=\ell$, where $\ell\geq 0$ is a real number, $ρ(x)$ is a nonnegative potential belonging to a certain Kato class, and $f(u)$ has a sublinear growth. We distinguish the cases $\ell>0$ and $\ell=0$ and we prove existence and uniqueness results if the potential $ρ(x)$ decays fast enough at infinity. Our arguments rely on comparison techniques and on a theorem of Brezis and Oswald for sublinear elliptic equations.

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Teodora Liliana Dinu. 2005-11-07. Entire solutions of sublinear elliptic equations in anisotropic media. https://arxiv.org/abs/math/0511183

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