Sturmian theorems for second order systems

Author:
W. Allegretto

Journal:
Proc. Amer. Math. Soc. **94** (1985), 291-296

MSC:
Primary 35B05; Secondary 35J45

DOI:
https://doi.org/10.1090/S0002-9939-1985-0784181-8

MathSciNet review:
784181

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Abstract: Sturmian theorem are established for weakly coupled elliptic systems generated in a bounded domain by the expressions , and Dirichlet boundary conditions. Here denotes the Laplace operator, and are matrices. We do not assume that are symmetric, but instead essentially require irreducible and . Estimates on the real eigenvalue of , with a positive eigenvector are then obtained as applications. Our results are motivated by recent theorems for ordinary differential equations established by Ahmad, Lazer and Dannan.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0784181-8

Keywords:
Sturmian theorem,
elliptic system,
eigenvalue,
positive operator

Article copyright:
© Copyright 1985
American Mathematical Society