2009/11/05 by A. Cañada, Antonio Canada, Canada, Antonio +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #math.CA
paper · pdf · doi:10.48550/arxiv.0911.1019
arxiv created 2009/11/05 · openalex publication_date 2009/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the study of some special minimization problems, where the Lagrange multiplier Theorem plays a fundamental role. This allows to obtain the optimal constants. Our applications include the Hill's equation where we give some new conditions on its stability properties and also the study of periodic and nonlinear problems at resonance where we show some new conditions which allow to prove the existence and uniqueness of solutions.