Topological Methods in Nonlinear Analysis

Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

Antonio Cañada and Salvador Villegas

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 45, Number 2 (2015), 309-326.

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1459343985

Digital Object Identifier
doi:10.12775/TMNA.2015.016

Mathematical Reviews number (MathSciNet)
MR3408825

Zentralblatt MATH identifier
1365.34042

Citation

Cañada, Antonio; Villegas, Salvador. Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations. Topol. Methods Nonlinear Anal. 45 (2015), no. 2, 309--326. doi:10.12775/TMNA.2015.016. https://projecteuclid.org/euclid.tmna/1459343985


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