Forced oscillation of third order nonlinear dynamic equations on time scales

• Autorzy: Baoguo Jia
• Języki publikacji: EN

Abstrakty

EN

Consider the third order nonlinear dynamic equation
$x^{ΔΔΔ}(t) + p(t)f(x) = g(t)$, (*)
on a time scale 𝕋 which is unbounded above. The function f ∈ C(𝓡,𝓡) 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
$Δ³x(n) + n^{α} |x|^γ sgn(n) = (-1)ⁿn^c$,
where α ≥ -1, γ > 0, c > 3, is oscillatory.

Kategorie tematyczne

• 39A10: Difference equations, additive
• 39A99: None of the above, but in this section
• 34K11: Oscillation theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 99
• Numer: 1
• Strony: 79-87

Daty

wydano

2010

Twórcy

autor

Baoguo Jia

• Department of Mathematics, Zhongshan University, Guangzhou, China 510275

Identyfikatory

DOI

10.4064/ap99-1-7