Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, we show how the cosmological constant Λ affects various astrophysical quantities important for large matter conglomeration in the universe. Among others we examine the effect of Λ on the polytropic equation of state for spherically symmetric...

Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, we show how the cosmological constant Λ affects various astrophysical quantities important for large matter conglomeration in the universe. Among others we examine the effect of Λ on the polytropic equation of state for spherically symmetric...

We are concerned with the Lane-Emden problem{−Δu=upinΩ,u>0inΩ,u=0on∂Ω, where Ω⊂R2 is a smooth bounded domain and p>1 sufficiently large. Improving some known asymptotic estimates on solutions, we prove non-degeneracy local uniqueness of multi-spikes positive solutions for general domains. Our methods mainly use ODE's theory, various Pohozaev identities, blow-up analysis properties Green's funct...

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...