Lyapunov inequality for elliptic equations involving limiting nonlinearities

Sergey A. Timoshin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This note deals with a generalization of the famous Lyapunov inequality giving a necessary condition for the existence of solutions to a boundary value problem for an ordinary differential equation. The problem we consider is closely related to a well-known problem on an asymptotic behavior of positive solutions of a class of semilinear elliptic equations of nearly critical Sobolev growth.

Original languageEnglish
Pages (from-to)139-142
Number of pages4
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Issue number8
Publication statusPublished - Aug 2010
Externally publishedYes


  • Critical exponents
  • Elliptic equations
  • Lyapunov inequality


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