Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials

We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an indefinite weight. In particular we are interested in the case where such a weight is positive in a ball and negative outside, or in the reversed situation. We extend the approach to elliptic equations in presence of Hardy potentials, i.e. to $$Delta u +rac{h(| extrm{x}|)}{| extrm{x}|^2} u+ f(u, | extrm{x}|)=0 $$ where $h$ is not necessarily constant. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.