A note on the inequality \(\Delta u\geq k(x)e^ u\) in \({\mathbb{R}}^ n\) (Q1825369)

This note is concerned with the problem of nonexistence of entire solutions for the differential inequality \[ (1)\quad \Delta u\geq k(x)e^ u,\quad x\in {\mathbb{R}}^ n, \] where \(n\geq 2\), \(\Delta\) is the n- dimensional Laplacian and k(x) is a nonnegative continuous function in \({\mathbb{R}}^ n\).