Positive Solutions of a Nonlinear Elliptic Equation Involving a Singular Term

In this work, we study the existence and uniqueness of positive solutions to the equation p u = f (|x|)/u(x), x R N , where N > p > 2.More precisely, under certain assumptions concerning the function f , we provide an answer to the question of global existence formulated in [14] by using the theory of invariant manifolds in dynamical systems and the energy method.In addition, we perform a detailed analysis of the asymptotic behavior of solutions by using logarithmic transformations.