Forced oscillation of third order nonlinear dynamic equations on time scales

Baoguo Jia

Baoguo Jia

Annales Polonici Mathematici, Tome 98 (2010), p. 79-87 / Harvested from The Polish Digital Mathematics Library

Résumé

Consider the third order nonlinear dynamic equation $x^{Δ Δ Δ} (t) + p (t) f (x) = g (t)$ , (*) on a time scale which is unbounded above. The function f ∈ C(,) is assumed to satisfy xf(x) > 0 for x ≠ 0 and be nondecreasing. We study the oscillatory behaviour of solutions of (*). As an application, we find that the nonlinear difference equation $Δ ³ x (n) + n^{α} {| x |}^{γ} s g n (n) = (- 1) ⁿ n^{c}$ , where α ≥ -1, γ > 0, c > 3, is oscillatory.

Publié le : 2010-01-01

Zbl 1209.34113

EUDML-ID : urn:eudml:doc:280285

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     title = {Forced oscillation of third order nonlinear dynamic equations on time scales},
     journal = {Annales Polonici Mathematici},
     volume = {98},
     year = {2010},
     pages = {79-87},
     zbl = {1209.34113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-1-7}
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Baoguo Jia. Forced oscillation of third order nonlinear dynamic equations on time scales. Annales Polonici Mathematici, Tome 98 (2010) pp. 79-87. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-1-7/