2009/06/05 by A. Cañada, Antonio Canada, Canada, Antonio +2
Computer Science · Mathematics · #34B05 #34B15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #math.CA #msc:34B05 #msc:34B15
paper · pdf · doi:10.48550/arxiv.0906.1091
17 pages. To appear in JEMS
arxiv created 2009/06/05 · openalex publication_date 2009/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of Lyapunov-type inequality for Neumann boundary conditions at higher eigenvalues. Our main result is derived from a detailed analysis about the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the use of suitable minimization problems. This method of proof allows to obtain new information on Lyapunov constants. For instance, we prove that as in the classical result by Lyapunov, the best constant is not attained. Additionally, we exploit the relation between Neumann boundary conditions and disfocality to provide new nonresonance conditions at higher eigenvalues.