Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, in general, the solution of the Lane-Emden equation can not be given analytically but only numerically. In this paper we give a good analytic approximate solution of the Lane-Emden equation. This approximation is very good for any finite polytropic index n and for the...

Piecewise quasilinearization methods for singular boundary-value problems in second-order ordinary differential equations are presented. These methods result in linear constant-coefficients ordinary differential equations which can be integrated analytically, thus yielding piecewise analytical solutions. The accuracy of the globally smooth piecewise quasilinear method is assessed by comparisons...

In this research study, a novel computational algorithm for solving second-order singular functional differential equation as generalization of the well-known Lane–Emden and differential-difference equations is presented by using Bessel bases. This technique depends on transforming problem into system algebraic unknown coefficients are determined solution will be known. The method tested severa...

We study qualitative properties for nonnegative solutions to a conformally invariant coupled system of fourth order equations involving critical exponents. For defined in the punctured space, there exist essentially two cases analyze. If origin is removable singularity, we use an integral moving spheres method prove that non-singular are rotationally invariant. More precisely, they product sphe...

In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of fact that Gravitational Decoupling allows decrease number degrees freedom once well known solution Einstein field is provided as seed so after demanding polytropic equation radial pressure system automatically closed. The not only extend both isotropic or ...

We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present proof of local existence positive radial solutions near $0$ under suitable conditions on $K$. Moreover, we provide a priori estimates $\infty $ when $r^{-\ell }K(r)$ for $\ell \ge -p$ is bounded $.