Entire solutions of sublinear elliptic equations in anisotropic media

Details Entire solutions of sublinear elliptic equations in anisotropic media Entire solutions of sublinear elliptic equations in anisotropic media

2005-11-07

arxiv.org/abs/math/0511183v1

Mathematics

Analysis of PDEs

Scientific paper

We study the nonlinear elliptic problem $-\Delta u=\rho (x)f(u)$ in $\RR^N$ ($N\geq 3$), $\lim\_{|x|\ri\infty}u(x)=\ell$, where $\ell\geq 0$ is a real number, $\rho(x)$ 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 $\rho(x)$ 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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