Description

• Title:
  Multiplicity of solutions to critical p-Laplace equations involving a Hardy potential
• Creator:
  Le, Diem Hang T.;
  Le, Phuong
• Description:
  In this paper, we prove the existence of at least $N$ pairs of nontrivial solutions to the doubly critical quasilinear elliptic problem \[ -\Delta_p u - \frac{\lambda}{|x|^p}|u|^{p-2}u =a(x)|u|^{p-2}u + |u|^{p^*-2}u \] in $\mathbb{R}^N$, as well as in smooth bounded domains, where $1< p< N$, $0< \lambda< (({N-p})/{p})^p$ and $a$ is strictly positive in a small ball. Our results hold under the assumption that $N\ge p^2$ and $\lambda$ and $\|a^+\|_{L^{N/p}}$ are small enough. To circumvent difficulties due to the lack of compactness of the problem, we combine Krasnosel'ski{\u\i}'s genus with a recent classification result by Oliva, Sciunzi, Vaira (J. Math. Pures Appl. {\bf 140} (2020), 89-109) and global compactness results by Li, Guo, Niu (Nonlinear Anal. {\bf 74} (2011), no.\ 4, 1445-1464).
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2025 Diem Hang T. Le, Phuong Le;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2025.02.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 65, No 1 (March 2025); 287 - 299;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/58855/41559 ;https://apcz.umk.pl/TMNA/article/view/58855/41560
• Subject:
  p-Laplace problems;
  critical Sobolev exponent;
  Hardy potential;
  multiplicity;
  Palais-Smale sequences;
  35J92, 35B33, 35B38
• Identifier: https://apcz.umk.pl/TMNA/article/view/58855
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other