Lyapunov inequality for elliptic equations involving limiting nonlinearities. (English) Zbl 1205.35070

Timoshin, Sergey A.

Proc. Japan Acad., Ser. A 86, No. 8, 139-142 (2010).

Summary: 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.

MSC:

35J25	Boundary value problems for second-order elliptic equations
35B33	Critical exponents in context of PDEs
35J62	Quasilinear elliptic equations

Keywords:

elliptic equations; critical exponents; Lyapunov inequality

References:

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