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Keywords:
canonical; noncanonical; oscillatory; nonoscillatory; principal system
canonical; noncanonical; oscillatory; nonoscillatory; principal system
Summary:
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.
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