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"Atkinson, F. V"
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Multiparameter eigenvalue problems : Sturm-Liouville theory
\"With special attention to the Sturm-Liouville theory, this book discusses the full multiparameter theory as applied to second-order linear equations. It considers the spectral theory of these multiparameter problems in detail for both the regular and singular cases. The text covers eignencurves, the essential spectrum, eigenfunctions, oscillation theorems, the distribution of eigencurves, the limit point, limit circle theory, and more. This text is the culmination of more than two decades of research by F.V. Atkinson, one of the masters in the field, and his successors, who continued his work after he passed away in 2002\"-- Provided by publisher.
Book
An oscillation criterion for linear second-order differential systems
This article is concerned with the oscillatory behavior at infinity of the solution y:[a,∞)→Rny:[a,\\infty ) \\to {{\\mathbf {R}}^n} of a system of nn second-order differential equations, y(t)y(t)=0,t∈[a,∞);Qy(t)y(t) = 0,\\;t \\in [a,\\infty );\\;Q is a continuous matrix-valued function on [a,∞)[a,\\infty ) whose values are real symmetric matrices of order nn. It is shown that the solution is oscillatory at infinity if (at least) n−1n - 1 eigenvalues of the matrix ∫atQ(t)dt\\smallint _a^tQ(t)\\;dt dt end to infinity as t→∞t \\to \\infty.
Journal Article
