Some results on weighted subquadratic Lane–Emden Elliptic Systems in unbounded domains

Abstract

We study a nonlinear elliptic system of Lane–Emden type in ${\mathbb{R}}^N,N\ge 3$, which is equivalent to a fourth order quasilinear elliptic equation involving a suitable ‘‘sublinear’’ term. Thanks to some compact imbeddings in weighted Sobolev spaces, existence and multiplicity results are proved by means of a generalized Weierstrass Theorem and a variant of the Symmetric Mountain Pass Theorem. These results apply in particular to a biharmonic equation under Navier conditions in ${\mathbb{R}}^N$.