Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2015Embargo end date: 01 Jan 2009Publisher:Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus UniversityJournal:Topological Methods in Nonlinear Analysis, volume 45, page 309 (issn: 1230-3429,

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Authors: Cañada, Antonio; Villegas, Salvador;

doi: 10.12775/tmna.2015.016 , 10.48550/arxiv.0906.1093

arXiv: 0906.1093

Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

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Abstract

This paper is devoted to the study of $L_p$ Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant $p \geq 1$. We consider ordinary and elliptic problems. The results obtained in the linear case are combined with Schauder fixed point theorem to provide new results about the existence and uniqueness of solutions for resonant nonlinear problems. The proof uses in a fundamental way the nontrivial relation between the best Lyapunov constants and the minimum value of some especial minimization problems.

17 pages

Related Organizations

University of Granada
Spain
Nicolaus Copernicus University
Poland

Keywords

34B15, 34B05, 35J20, 35J25, 35J65, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Analysis of PDEs (math.AP)

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