Abstract
We study the oscillatory behavior of solutions of the fourth-order Emden–Fowler equation: (E) y (iv)+q(t)|y|α sgny=0, where α>1 and q(t) is a positive continuous function on [t 0,∞), t 0>0. Our main results Theorem 2 – if (q(t)t (3α+5)/2)′≥0, then equation (E) has oscillatory solutions; Theorem 3 – if lim t→∞ q(t)t 4+λ(α-1)=0, λ>0, then every solution y(t) of equation (E) is either non-oscillatory or satisfies limsup t→∞ t -μ+i|y (i)(t)|=∞ for μ<λ and i=0,1,2,3,4. These results complement those given by Kura for equation (E) when q(t)<0 and provide analogues to the results of the second-order equation, y ′′+q(t)|y|α sgny=0,α>1.
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Mathematics Subject Classification (2000)
34C10, 34C15
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Ou, C., Wong, J. Oscillation and non-oscillation theorems for superlinear Emden–Fowler equations of the fourth order. Ann. Mat. Pura Appl. IV. Ser. 183, 25–43 (2004). https://doi.org/10.1007/s10231-003-0079-z
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DOI: https://doi.org/10.1007/s10231-003-0079-z