# Radial solutions of scaling invariant nonlinear elliptic equations with mixed reaction terms

## TL;DR

This paper investigates the existence and non-existence of positive radial solutions to a class of nonlinear elliptic equations with mixed reaction terms, depending on parameters M and p, revealing conditions for ground states and singular solutions.

## Contribution

It provides new criteria for the existence and non-existence of solutions to a class of nonlinear elliptic equations with mixed reaction terms based on parameters M and p.

## Key findings

- Existence of ground states under certain M and p values.
- Non-existence of solutions with singularity at 0 for other parameter ranges.
- Characterization of solutions based on the parameters M and p.

## Abstract

We study global properties of positive radial solutions of --$\Delta$u = up +M |$\nabla$u|p+1 in RN wherep > 1 and M is a real number. We prove the existence or the non-existence of ground states and of solutions with singularity at 0 according to the values of M and p.