Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

Details Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

2009-06-05

arxiv.org/abs/0906.1093v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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