Geodesic
On nonoscillation of canonical or noncanonical disconjugate functional equations
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 627-639 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Qualitative comparison of the nonoscillatory behavior of the equations \[ L_ny(t) + H(t,y(t)) = 0 \] and \[ L_ny(t) + H(t,y(g(t))) = 0 \] is sought by way of finding different nonoscillation criteria for the above equations. $L_n$ is a disconjugate operator of the form \[ L_n = \frac{1}{p_n(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{1}{p_{n-1}(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \ldots \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{\cdot }{p_0(t)}. \] Both canonical and noncanonical forms of $L_n$ have been studied.
Qualitative comparison of the nonoscillatory behavior of the equations \[ L_ny(t) + H(t,y(t)) = 0 \] and \[ L_ny(t) + H(t,y(g(t))) = 0 \] is sought by way of finding different nonoscillation criteria for the above equations. $L_n$ is a disconjugate operator of the form \[ L_n = \frac{1}{p_n(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{1}{p_{n-1}(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \ldots \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{\cdot }{p_0(t)}. \] Both canonical and noncanonical forms of $L_n$ have been studied.
Classification : 34K11, 34K15, 34K25, 35J30, 35R10
Keywords: canonical; noncanonical; oscillatory; nonoscillatory; principal system 
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Singh, Bhagat. On nonoscillation of canonical or noncanonical disconjugate functional equations. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 627-639. http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a14/

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