A priori estimates for elliptic equations with reaction terms involving the function and its gradient

TL;DR

This paper investigates solutions to elliptic equations with reaction terms involving the function and its gradient, establishing a priori estimates and conditions for existence or non-existence of ground states.

Contribution

It provides new a priori estimates and existence results for elliptic equations with combined reaction terms involving the function and its gradient.

Findings

Established a priori bounds for solutions.

Identified conditions for existence of ground states.

Proved non-existence results under certain parameters.

Abstract

We study local and global properties of solutions of --$\Delta$u = u p + M ||u| q in a domain $\Omega$ of R N , in the range min{p, q} > 1 and M $\in$ R. We prove a priori estimates and existence or non-existence of ground states.