Positive solutions to the sublinear Lane-Emden equation are isolated

Lorenzo Brasco, Guido De Philippis, Giovanni Franzina

Research output: Contribution to journalArticlepeer-review


We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

Original languageEnglish (US)
Pages (from-to)1940-1972
Number of pages33
JournalCommunications in Partial Differential Equations
Issue number10
StatePublished - 2021


  • Cone condition
  • Lane-Emden equation
  • constrained critical points
  • eigenvalues

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Positive solutions to the sublinear Lane-Emden equation are isolated'. Together they form a unique fingerprint.

Cite this