Displaying similar documents to “On transformations of self-adjoint linear differential systems and their reciprocals”

Interval oscillation criteria for second order self-adjoint matrix differential systems with damping

Qigui Yang (2002)

Annales Polonici Mathematici

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By using the generalized Riccati technique and the averaging technique, we establish new oscillation criteria for the second order self-adjoint matrix differential system with damping (P(t)Y'(t))' + r(t)P(t)Y'(t) + Q(t)Y(t) = 0, t ≥ t₀. The criteria are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t₀,∞), rather than on the whole half-line. In particular, our results complement...

Generalized reciprocity for self-adjoint linear differential equations

Ondřej Došlý (1995)

Archivum Mathematicum

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Let L ( y ) = y ( n ) + q n - 1 ( t ) y ( n - 1 ) + ⋯ + q 0 ( t ) y , t ∈ [ a , b ) , be an n -th order differential operator, L * be its adjoint and p , w be positive functions. It is proved that the self-adjoint equation L * p ( t ) L ( y ) = w ( t ) y is nonoscillatory at b if and only if the equation L w - 1 ( t ) L * ( y ) = p - 1 ( t ) y is nonoscillatory at b . Using this result a new necessary condition for property BD of the self-adjoint differential operators with middle terms is obtained.