Lyapunov inequalities for Partial Differential Equations at radial higher eigenvalues

2011/09/23 by A. Cañada, Antonio Canada, Canada, Antonio +2
Computer Science · Engineering · Mathematics · #35B07 #35J20 #35J25 #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.AP #msc:35B07 #msc:35J20 #msc:35J25

paper · pdf · doi:10.48550/arxiv.1109.5020

15 pages

arxiv created 2011/09/23 · openalex publication_date 2011/09/23 · arxiv updated 2011/09/26 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the study of L_p Lyapunov-type inequalities ( 1 ≤ p ≤ +∞) for linear partial differential equations at radial higher eigenvalues. More precisely, we treat the case of Neumann boundary conditions on balls in \real^N. It is proved that the relation between the quantities p and N/2 plays a crucial role to obtain nontrivial and optimal Lyapunov inequalities. By using appropriate minimizing sequences and a detailed analysis about the number and distribution of zeros of radial nontrivial solutions, we show significant qualitative differences according to the studied case is subcritical, supercritical or critical.

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