αu(0)−β u(0) = 0, γu(1)+ δu(1) = 0, (2) where α,β ,γ,δ ≥ 0,λ ∈ R and ρ := γβ + αγ + αδ > 0; p ∈ C((0,1), [0,∞)) and may be singular at t = 0,t = 1. When λ < 0, see [3,4,7,8] for the result concerning the above problem. When λ > 0, [6] shows the existence and uniqueness to (1) and (2) in the case of β = δ = 0 by means of the shooting method. For the following problem u + p(t)u−λ(t)+ q(t)u(t) = 0...

Article history: Received 28 May 2010 Available online 16 September 2010 Submitted by Goong Chen

In this Letter, we apply the homotopy-perturbation method (HPM) to obtain approximate analytical solutions of the time-dependent Emden– Fowler type equations. We also present a reliable new algorithm based on HPM to overcome the difficulty of the singular point at x = 0. The analysis is accompanied by some linear and nonlinear time-dependent singular initial value problems. The results prove th...

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We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in ...

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