On asymptotic behaviour of oscillatory solutions for fourth order differential equations
Texas State University-San Marcos, Department of Mathematics
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.
Oscillatory solution, Asymptotic behaviour
Padhi, S., & Qian, C. (2007). On asymptotic behaviour of oscillatory solutions for fourth order differential equations. <i>Electronic Journal of Differential Equations, 2007</i>(22), pp. 1-5.