A dynamical system approach for Lane-Emden type problems

``The book is aimed for graduate students interested in Partial Differential Equations and/or Dynamical Systems. We tried to gather a self contained and detailed analysis on the subject, in addition to several references, in such a way to ease the experience of the reader. ``Here we exploit the classification of radial positive solutions for a class of fully nonlinear problems. Our approach is entirely based on the analysis of the dynamics induced by an autonomous quadratic system, which is obtained after a suitable transformation. This method allows us to treat both regular and singular solutions in a unified way. It applies to define critical exponents, from which existence and nonexistence of solutions are completely characterized. ``It is our goal to enable the reader to identify all trajectories produced by the dynamical system and translate it into positive radial solutions of the corresponding second order partial differential equations problem. We will deal with solutions in a ball, the whole space, exterior domains, and annuli.