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Peer-reviewedCC BYElectronic Journal of Differential Equations

Existence and uniqueness of solutions to Hardy-Henon boundary-value problems

  • Xiyou Cheng1
  • Huijuan Shao2
  • Lei Wei2
  • Meihua Yang3
  1. 1Lanzhou Univ. Lanzhou, Gansu, China
  2. 2Jiangsu Normal Univ.y, Xuzhou, Jiangsu, China
  3. 3Huazhong Univ. of Science and Tech., Wuhan, Hubei, China
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Abstract

We consider the elliptic equation −Δ u=d(x)α up, x∈ Ω (or x∈ℝN∖ Ω̅), where α, p ∈ ℝ, d(x) = dist (x,∂Ω) and Ω⊂ℝN (N≥ 3) is a bounded smooth domain. We establish estimates for the positive solutions when 1< p< fracN+2N−2, and the nonexistence of positive solutions for exterior domains. For the corresponding Dirichlet problem we show the existence and uniqueness of positive solutions.

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Cite

BibTeXRIS
BibTeX
@article{cheng2026existence,
  title = {{Existence and uniqueness of solutions to Hardy-Henon boundary-value problems}},
  author = {Xiyou Cheng and Huijuan Shao and Lei Wei and Meihua Yang},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = sep,
  url = {http://ejde.math.txstate.edu/Volumes/2026/72/abstr.html},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Existence and uniqueness of solutions to Hardy-Henon boundary-value problems
AU  - Xiyou Cheng
AU  - Huijuan Shao
AU  - Lei Wei
AU  - Meihua Yang
PY  - 2026
DA  - 2026/09/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/72/abstr.html
AB  - We consider the elliptic equation −Δ u=d(x)^α u^p, x∈ Ω (or x∈ℝ^N∖ Ω̅), where α, p ∈ ℝ, d(x) = dist (x,∂Ω) and Ω⊂ℝ^N (N≥ 3) is a bounded smooth domain. We establish estimates for the positive solutions when 1< p< fracN+2N−2, and the nonexistence of positive solutions for exterior domains. For the corresponding Dirichlet problem we show the existence and uniqueness of positive solutions.
SN  - 1072-6691
ER  -