Lie Algebra Representation, Conservation Laws and Some Invariant Solutions for a Generalized 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.

Multiple solutions for boundary value problems of a discrete generalized Emden-Fowler equation

By using critical point theory, some new sufficient conditions for the existence of at least 2N distinct solutions to boundary value problems of a discrete generalized Emden–Fowler equation are obtained. © 2009 Elsevier Ltd. All rights reserved.

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...

Quasi-Lie schemes and Emden–Fowler equations

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from t...

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