Singular initial value problems are investigated. We extend a decomposition method for di¤erent type Emden-Fowler-like equations. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method. The solutions are constructed in the form of a convergent series.

In this article, we presented a new approach deduced from He’s homotopy perturbation method (HPM) to obtain exact and/or approximate analytical solutions of Emden–Fowler type equations. The results reveal that the proposed algorithm is very effective and in most cases yield exact solutions in the first approximation. Some examples are given to illustrate the new approach.

We derive a monotonicity formula for solutions of the fractional Hénon-Lane-Emden equation (−∆)u = |x|a|u|p−1u R where 0 < s < 2, a > 0 and p > 1. Then we apply this formula to classify stable solutions of the above equation.

In this article, we tried to get the solution of a class Lane Emden type equations by using Fourier Decomposition Method. This method is obtained transform and Adomian (FADM) together.

This paper is devoted to proposing numerical algorithms based on the use of tau and collocation procedures, two widely used spectral approaches for treatment initial high-order linear non-linear equations singular type, especially those Emden–Fowler type. The class modified Chebyshev polynomials third-kind constructed. generalizes polynomials. A new formula that expresses first-order derivative...

The purpose of this study is to provide a mathematical construction based on the novel singular perturbed model second kind (NSPM-SK) using standard form Lane–Emden. Lane–Emden types models have abundant applications in astrophysics. inclusive features are provided perturbed, pantograph, point together and shape factor NSPM-SK. These become more complicated by these factors through artificial n...

We consider the second order differential equation ( a(t)|x′|α sgn x′ )′ + b(t)|x| sgn x = 0 in the super-linear case α < β. We prove the existence of the so-called intermediate solutions and we discuss their coexistence with other types of nonoscillatory and oscillatory solutions. Our results are new even for the Emden–Fowler equation (α = 1).

We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5 core-radii and to 0.1% within 10 core-radii.