Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

Salvador Villegas, Antonio Cañada

DOI: http://dx.doi.org/10.12775/TMNA.2015.016

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.

Keywords


Neumann boundary value problems; matrix Lyapunov inequalities; ordinary differential equations; elliptic partial differential equations; resonant problems

Full Text:

Full Text

Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism