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Liouville type theorems for Hardy–Hénon equations with concave nonlinearities

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  • Wei Dai
  • Guolin Qin

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.

Suggested Citation

  • Wei Dai & Guolin Qin, 2020. "Liouville type theorems for Hardy–Hénon equations with concave nonlinearities," Mathematische Nachrichten, Wiley Blackwell, vol. 293(6), pages 1084-1093, June.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:6:p:1084-1093
    DOI: 10.1002/mana.201800532
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    Cited by:

    1. Yoshikazu Giga & Quốc Anh Ngô, 2022. "Exhaustive existence and non-existence results for Hardy–Hénon equations in $${{\,\mathrm{{\textbf{R}}}\,}}^n$$ R n," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-38, December.

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