In this paper, Singular initial value problems are investigated by using Taylor series method. The solutions are constructed in the form of a convergent series. The method is applied to Emden-Fowler and Lane-Emden equations.

By using critical point theory, some new sufficient conditions for the existence of at least 2N distinct solutions to boundary value problems of a discrete generalized Emden–Fowler equation are obtained. © 2009 Elsevier Ltd. All rights reserved.

The existence of a class of nonoscillatory solutions for a generalized Emden–Fowler differential equation is studied. Some analogies and discrepancies between the continuous and discrete case are also discussed. AMS subject classification: Primary 34C10, Secondary 34C15, 39A10.

Abstract We study the asymptotic behavior of local solutions to Yamabe equation near an isolated singularity, when metric is not conformally flat. prove that, in dimension 6, any solution asymptotically close a Fowler solution, which extension same result for lower dimensions by F.C. Marques 2008.