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June  2006, 5(2): 321-336. doi: 10.3934/cpaa.2006.5.321

Analysis of singular boundary value problems for an Emden-Fowler equation

P. Lima 1, and  L. Morgado 2,

1. 

Centro de Matemática Aplicacoes, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa
2. 

Departamento de Matemática, Universidade de Trás-os-Montes e Alto Douro, Apartado 1013, 5000-311 Vila Real, Portugal

Received  March 2005 Revised  June 2005 Published  March 2006

In this work we are concerned about a second order nonlinear ordinary differential equation. Our main purpose is to describe one-parameter families of solutions of this equation which satisfy certain boundary conditions. These one-parameter families of solutions are obtained in the form of asymptotic or convergent series. The series expansions are then used to approximate the solutions of two boundary value problems. We are specially interested in the cases where these problems are degenerate with respect to the unknown function and/or to the independent variable. Lower and upper solutions for each of the considered boundary value problems are obtained and, in certain particular cases, a closed formula for the exact solution is derived. Numerical results are presented and discussed.
Keywords: Singular boundary value problems, one-parameter families of solutions, convergent Lyapunov series, shooting methods..
Mathematics Subject Classification: 65L0.
Citation: P. Lima, L. Morgado. Analysis of singular boundary value problems for an Emden-Fowler equation. Communications on Pure & Applied Analysis, 2006, 5 (2) : 321-336. doi: 10.3934/cpaa.2006.5.321
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