Liouville type theorems for Hardy–Hénon equations with concave nonlinearities

Wei Dai and Guolin Qin

Mathematische Nachrichten, 2020, vol. 293, issue 6, 1084-1093

Abstract: In this paper, we are concerned with the Hardy–Hénon equations −Δu=|x|aupandΔ2u=|x|aupwith a∈R and p∈(0,1]. Inspired by Serrin and Zou [25], we prove Liouville theorems for nonnegative solutions to the above Hardy–Hénon equations (Theorem 1.1 and Theorem 1.3), that is, the unique nonnegative solution is u≡0.

Date: 2020
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