Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations
KeywordsNeumann boundary value problems, matrix Lyapunov inequalities, ordinary differential equations, elliptic partial differential equations, resonant problems
AbstractThis 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.
How to Cite
VILLEGAS, Salvador & CAÑADA, Antonio. Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations. Topological Methods in Nonlinear Analysis [online]. 1 June 2015, T. 45, nr 2, s. 309–326. [accessed 3.2.2023]. DOI 10.12775/TMNA.2015.016.
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