On asymptotic behaviour of oscillatory solutions for fourth order differential equations
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We establish sufficient conditions for the linear differential equations of fourth order
(r(t)y‴ (t))′ = α(t)y(t) + b(t)y′(t) + c(t)y″(t) + ƒ(t)
so that all osillatory solutions of the equation satisfy
limt→∞ y(t) = limt→∞ y′(t) = limt→∞ y″(t) = limt→∞ r(t)y‴(t) = 0,
where r : [0, ∞) → (0, ∞), α, b, c and ƒ : [0, ∞) → R are continuous functions. A suitable Green's function and its estimates are used in this paper.
CitationPadhi, S., & Qian, C. (2007). On asymptotic behaviour of oscillatory solutions for fourth order differential equations. Electronic Journal of Differential Equations, 2007(22), pp. 1-5.
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