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PreprintCC BY 4.0arXiv

Lane-Emden equation for the superposition of a local and nonlocal operator with the "wrong sign"

  • Stefano Biagi
  • Eugenio Vecchi
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Abstract

We consider the Lane-Emden equation associated with the operator −Δ− γ (−Δ)s (for positive γ). First we consider the equation in the entire space and we prove that no Serrin-type critical exponent arises in the H1(ℝn) framework. Secondly we consider the problem settled in an open, bounded and connected set and we prove the existence of a positive solution for sufficiently small s.

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Cite

BibTeXRIS
BibTeX
@misc{biagi2026laneemden,
  title = {{Lane-Emden equation for the superposition of a local and nonlocal operator with the "wrong sign"}},
  author = {Stefano Biagi and Eugenio Vecchi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.42070},
  eprint = {2610.42070},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.42070},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Lane-Emden equation for the superposition of a local and nonlocal operator with the "wrong sign"
AU  - Stefano Biagi
AU  - Eugenio Vecchi
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.42070
UR  - https://arxiv.org/abs/2610.42070
AB  - We consider the Lane-Emden equation associated with the operator −Δ− γ (−Δ)^s (for positive γ). First we consider the equation in the entire space and we prove that no Serrin-type critical exponent arises in the H^1(ℝ^n) framework. Secondly we consider the problem settled in an open, bounded and connected set and we prove the existence of a positive solution for sufficiently small s.
ER  -