Liouville-type Theorems for Polyharmonic Hénon-Lane-Emden System

Liouville theorems for stable Lane-Emden systems and biharmonic problems

We examine the elliptic system given by −∆u = v, −∆v = u, in R , (1) for 1 < p ≤ θ and the fourth order scalar equation ∆u = u, in R , (2) where 1 < θ. We prove various Liouville type theorems for positive stable solutions. For instance we show there are no positive stable solutions of (1) (resp. (2)) provided N ≤ 10 and 2 ≤ p ≤ θ (resp. N ≤ 10 and 1 < θ). Results for higher dimensions are also...

On Lane-emden Type Systems

We consider a class of singular systems of Lane-Emden type      ∆u + λu p 1 v q 1 = 0, x ∈ D, a smooth domain in R n. In case the system is sublinear we prove existence of a positive solution. If D is a ball in R n , we prove both existence and uniqueness of positive radially symmetric solution.

Ultraspherical Wavelets Method for Solving Lane-emden Type Equations

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

MODIFICATION OF THE OPTIMAL HOMOTOPY ASYMPTOTIC METHOD FOR LANE-EMDEN TYPE EQUATIONS

In this paper, modication of the optimal homotopy asymptotic method (MOHAM) is appliedupon singular initial value Lane-Emden type equations and results are compared with the available exactsolutions. The modied algorithm give the exact solution for dierential equations by using one iterationonly.

Numerical method for solving Lane – Emden type equationsarising in astrophysics