Some New Results on Subquadratic Lane–Emden Elliptic Systems

Abstract

We deal with a nonlinear elliptic weighted system of Lane–Emden type in \(\mathbb R^N\), \(N \ge 3\), by exploiting its equivalence with a fourth-order quasilinear elliptic equation involving a suitable “sublinear” term. By overcoming the loss of compactness of the problem with some compact imbeddings in weighted \(L^p\)-spaces, we establish existence and multiplicity results by means of a generalized Weierstrass Theorem and a variant of the Symmetric Mountain Pass Theorem stated by R. Kajikiya for subquadratic functionals. These results, which generalize previous ones stated by the same authors, apply in particular to a biharmonic equation under Navier conditions in \(\mathbb R^N\).