On the positive solutions of an Emden-type elliptic equation

On Stable Solutions of the Fractional Henon-lane-emden Equation

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.

On the Positive Solutions of the Free-Boundary Problem for Emden-Fowler Type Equations

On the uniqueness of positive solution of an elliptic equation

This work deals with the uniqueness of positive solution for an elliptic equation whose nonlinearity satisfies an specific monotony property. In order to prove the main result, we employ a change of variable used in previous papers and the maximum principle.

Bubbling Solutions for an Anisotropic Emden-Fowler Equation

We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quanti...

Approximate solutions of Emden-Fowler type equations

Singular initial value problems are investigated. We extend a decomposition method for di¤erent type Emden-Fowler-like equations. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method. The solutions are constructed in the form of a convergent series.