Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains

Details Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains

2010-08-28

arxiv.org/abs/1008.4871v4

Mathematics

Analysis of PDEs

46 pages

Scientific paper

Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the existence of positive eigenfunctions satisfying Dirichlet boundary conditions. Relations between these principal eigenvalues, their simplicity and several other properties are further discussed.

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