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.
"Lyapunov inequality for elliptic equations involving limiting nonlinearities." Proc. Japan Acad. Ser. A Math. Sci. 86 (8) 139 - 142, October 2010. https://doi.org/10.3792/pjaa.86.139