Generalized Emden-Fowler equations of subcritical growth

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.

On Nodal Solutions to Generalized Emden-fowler Equations

We introduce a new variational method in order to derive results concerning existence and nodal properties of solutions to superlinear equations, and we focus on applications to the equation where h is a Caratheodory function which is odd in u. In the particular case where h is radially symmetric, we prove, for given n 2 N, the existence of a solution having precisely n nodal domains, whereas s...

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.

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...

Symmetry and nonexistence results for Emden-Fowler equations in cones