On a generalized Sturm theorem
نویسنده
چکیده
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 complex n-dimensional vector space C n and p2m is the symmetry represented by diag (In−ν ,−Iν) for some integer 0 ≤ ν ≤ n.
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