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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)

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J99 Elliptic equations and elliptic systems
35B50 Maximum principles in context of PDEs
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