In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singu...

A generator of Lie point symmetries admitted by a Lane–Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane–Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary c...

In this study, a high-order compact finite difference method is used to solve Lane–Emden equations with various boundary conditions. The norm use first-order scheme approximate Neumann and Robin conditions, but that compromises the accuracy of entire scheme. As result, new higher-order schemes for approximating conditions are developed in work. We test applicability performance using different ...