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 $.

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...

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...

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu+ u = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method. Keywords—Positive Solutions; Newton’s Method; Contractor Iteration Method; Eigenpairs.

We compute multiprecision solutions of the Lane–Emden equation. This differential equation arises when introducing the well-known polytropic model into the equation of hydrostatic equilibrium for a nondistorted star. Since such multiprecision computations are time-consuming, we apply to this problem parallel programming techniques and thus the execution time of the computations is drastically r...

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 paper, we establish two kinds of Emden–Fowler type equations of third order. We investigate the linear and the nonlinear third-order equations, with specified initial conditions, by using the systematic variational iteration method. We corroborate this study by investigating several Emden–Fowler type examples with initial value conditions.