Lyapunov inequality for elliptic equations involving limiting nonlinearities

Sergey A. Timoshin

doi:10.3792/pjaa.86.139

Lyapunov inequality for elliptic equations involving limiting nonlinearities

Sergey A. Timoshin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	139-142
Number of pages	4
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	86
Issue number	8
DOIs	https://doi.org/10.3792/pjaa.86.139
Publication status	Published - Aug 2010
Externally published	Yes

Keywords

Critical exponents
Elliptic equations
Lyapunov inequality

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10.3792/pjaa.86.139

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title = "Lyapunov inequality for elliptic equations involving limiting nonlinearities",

abstract = "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.",

keywords = "Critical exponents, Elliptic equations, Lyapunov inequality",

author = "Timoshin, \{Sergey A.\}",

year = "2010",

month = aug,

doi = "10.3792/pjaa.86.139",

language = "English",

volume = "86",

pages = "139--142",

journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",

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T1 - Lyapunov inequality for elliptic equations involving limiting nonlinearities

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AB - 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.

KW - Critical exponents

KW - Elliptic equations

KW - Lyapunov inequality

UR - https://www.scopus.com/pages/publications/77958613660

U2 - 10.3792/pjaa.86.139

DO - 10.3792/pjaa.86.139

M3 - Article

AN - SCOPUS:77958613660

SN - 0386-2194

VL - 86

SP - 139

EP - 142

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

IS - 8

ER -

Lyapunov inequality for elliptic equations involving limiting nonlinearities

Abstract

Keywords

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