Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues

Autor:	Canada, Antonio, Villegas, Salvador
Rok vydání:	2009
Předmět:	Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs 34B05 34B15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 17 pages. To appear in JEMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0906.1091 Zobrazit plný text záznamu View this record from Arxiv