Remarks on nonexistence of solutions of mixed sublinear and superlinear elliptic equation in

In this note, we consider the quasilinear elliptic equation ± Δ p u = h ( x ) u m + H ( x ) u n in R N ( N ⩾ 3 ), where 0 < m ⩽ p − 1 < n . We establish conditions sufficient to ensure the nonexistence of nonnegative entire solutions, which improves a result of A.V. Lair [A.V. Lair, Large solutions of mixed sublinear–superlinear elliptic equations, J. Math. Anal. Appl. 346 (2008) 99–106].