Oscillation of fourth-order strongly noncanonical differential equations with delay argument
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Abstract The aim of this paper is to study oscillatory properties of the fourth-order strongly noncanonical equation of the form $$ \bigl(r_{3}(t) \bigl(r_{2}(t) \bigl(r_{1}(t)y'(t) \bigr)' \bigr)' \bigr)'+p(t)y \bigl( \tau (t) \bigr)=0, $$ ( r 3 ( t ) ( r 2 ( t ) ( r 1 ( t ) y ′ ( t ) ) ′ ) ′ ) ′ + p ( t ) y ( τ ( t ) ) = 0 , where $\int ^{\infty }\frac{1}{r_{i}(s)}\,\mathrm {d}{s}<\infty $ ∫ ∞ 1 r i ( s ) d s < ∞ , $i=1,2,3$ i = 1 , 2 , 3 . Reducing possible classes of the nonoscillatory solutions, new oscillatory criteria are established.
2009 ◽
Vol 59
(2)
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pp. 353-370
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