Matrix Riccati equations and matrix Sturm–Liouville problems
Journal of Differential Equations, 2004 Let \(H_k\) denotes the set of all Hermitian \(k\times k\)-matrices. Let \(P, Q, R: [a, b] \to H_k\) be integrable functions and let \(\alpha \in \mathbb R\). Consider the matrix Sturm-Liouville eigenvalue problem \[ u' = Rv, \quad v' = -(\lambda P + Q) u, \tag{1} \] \[ u(a) = 0, u(b) \cos (\alpha /2) = v(b) \sin (\alpha /2). \tag{2} \] Let \(\lambda_0
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Constants in the oscillation theory of higher order Sturm-Liouville differential equations
Electronic Journal of Differential Equations, 2002 We find the the exact value of a constant in some oscillation criteria for the higher order Sturm-Liouville differential equation $$ (-1)^{n}(t^alpha y^{(n)})^{(n)}=q(t)y . $$ We also study some general aspects in the oscillation theory of this equation.
Ondrej Dosly
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