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We provide the structure of regular/singular fast/slow decay radiallysymmetric solutions for a class of superlinear elliptic equations with an in-definite weight on the nonlinearity f (u, r). In particular we are interestedin the case where f is positive in a ball and negative outside, or in the re-versed situation. We extend the approach to elliptic equations in presence ofHardy potentials. By the use of Fowler transformation we study thecorresponding dynamical systems, presenting the construction of invariantmanifolds when the global existence of solutions is not ensured.

Entire solutions of superlinear problems with indefinite weights and Hardy potentials