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.

Abstract We prove that the Dirichlet problem for Lane–Emden equation in a half-space has no positive solution is monotone normal direction. As consequence, this does not admit any classical bounded on finite strips. This question long history and our result solves long-standing open problem. Such nonexistence was previously available only solutions or under restriction power nonlinearity. The e...

This paper deals with the following critical elliptic systems of Hamiltonian type, which are variants Lane-Emden and analogous to prescribed curvature problem:{−Δu1=K1(y)u2p,y∈RN,−Δu2=K2(y)u1q,y∈RN,u1,u2>0, where N≥5,p,q∈(1,∞) 1p+1+1q+1=N−2N, K1(y) K2(y) positive radial potentials. At first, under suitable conditions on K1,K2 certain range exponents p,q, we construct an unbounded sequence non-r...