Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation

The Generalized Emden-Fowler Equation

We give the description of nonlinear nonautonomous ordinary differential equations of order n with a so-called reducible linear part. The group classification of generalized Emden-Fowler equations of the mentioned class is done. We have found such laws of the variation of f(x) that the equation admits one, two, or tree one-parameter Lie groups.

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.

Existence of Solutions to Boundary Value Problems for the Discrete Generalized Emden-Fowler Equation

Existence and Uniqueness of Local Weak Solutions for the Emden-fowler Wave Equation in One Dimension

In this article we consider the existence and uniqueness of local weak solutions to the Emden-Fowler type wave equation tutt − uxx = |u|p−1u in [1, T ]× (a, b) with initial-boundary value conditions in a finite time interval.