Entire large solutions for semilinear elliptic equations

Details Entire large solutions for semilinear elliptic equations Entire large solutions for semilinear elliptic equations

2011-11-09

arxiv.org/abs/1111.2207v1

Mathematics

Analysis of PDEs

Scientific paper

We analyze the semilinear elliptic equation $\Delta u=\rho(x) f(u)$, $u>0$ in
${\mathbf R}^D$ $(D\ge3)$ when $f$ grows superlinearly (resp. $\rho$ decays
superquadratically) at infinity. A particular emphasis is put on the
qualitative study of entire large solutions, that is, solutions $u$ such that
$\lim_{|x|\to+\infty}u(x)=+\infty$.

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