On a Generalized Sturm Theorem
نویسندگان
چکیده
منابع مشابه
On a generalized Sturm theorem
Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm theorem for indefinite systems with Dirichlet boundary conditions of the form p2m du dx + p2m−2(x) du dx + · · ·+ p1(x) du dx + p0(x)u = 0, where pi is a smooth path of matrices on the comple...
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We have formalised the Sturm-Tarski theorem (also referred as the Tarski theorem): Given polynomials p, q ∈ R[x], the Sturm-Tarski theorem computes the sum of the signs of q over the roots of p by calculating some remainder sequences. Note, the better-known Sturm theorem is an instance of the Sturm-Tarski theorem when q = 1. The proof follows the classic book by Basu et al. [1] and Cyril Cohen’...
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ژورنال
عنوان ژورنال: Advanced Nonlinear Studies
سال: 2010
ISSN: 2169-0375,1536-1365
DOI: 10.1515/ans-2010-0111