### 1998-28

by Bandle, C., Bordag, L. A..

**Series:** 1998-28, Preprints

- MSC:
- 34A34 Nonlinear equations and systems, general
- 35J60 Nonlinear elliptic equations

**Abstract:**

By means of the tools from invariant theory we prove the equivalence theorem for Emden equations under the general point transformations. We apply this theory to the Emden-Fowler equations in $\Bbb{R}^N$ and in $\Bbb{S}^3$ and to the Matukuma equation. The advantage of this method is that it provides a complete picture of all possible transformations which leave certain equations invariant. It also allows us to classify certain types of equations and to discuss their connexions to autonomous and Painlevé equation.

**Keywords:**

Emden equation, equivalence classes, point transformations, invariant theory.