LAUSR

We deal with a nonlinear elliptic weighted system of Lane–Emden type in $$\mathbb R^N$$RN, $$N \ge 3$$N≥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 $$L^p$$Lp-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 $$\mathbb R^N$$RN.