Birindelli, I.; Mitidieri, E.; Sweers, G. The existence of the principal eigenvalue for cooperative elliptic systems in a general domain. (English. Russian original) Zbl 0940.35147 Differ. Equations 35, No. 3, 326-334 (1999); translation from Differ. Uravn. 35, No. 3, 325-333 (1999). The existence of the principal eigenfunction of the vector-valued elliptic eigenvalue problem \[ (L-H)\Phi=\lambda B\Phi \] in \(\Omega\), \(\Phi=0\) on \(\partial \Omega\), and its relationship with the maximum principle is investigated. The operator \(L\) is a diagonal matrix consisting of uniformly elliptic second-order partial differential operators and \(H\) and \(B\) are cooperative matrices with entries from \(C(\overline{\Omega})\). The domain \(\Omega\subset \mathbb{R}^n\) is bounded. Any regularity condition is supposed on the boundary. Reviewer: J.DiblĂk (Brno) Cited in 18 Documents MSC: 35P15 Estimates of eigenvalues in context of PDEs 35J99 Elliptic equations and elliptic systems 35B50 Maximum principles in context of PDEs Keywords:principal eigenvalue; elliptic system; principal eigenfunction PDFBibTeX XMLCite \textit{I. Birindelli} et al., Differ. Equations 35, No. 3, 326--334 (1999; Zbl 0940.35147); translation from Differ. Uravn. 35, No. 3, 325--333 (1999)