On Asymptotic Behaviour of Oscillatory Solutions for Fourth Order Differential Equations
نویسندگان
چکیده
We establish sufficient conditions for the linear differential equations of fourth order (r(t)y′′′(t))′ = a(t)y(t) + b(t)y′(t) + c(t)y′′(t) + f(t) so that all oscillatory solutions of the equation satisfy lim t→∞ y(t) = lim t→∞ y′(t) = lim t→∞ y′′(t) = lim t→∞ r(t)y′′′(t) = 0, where r : [0,∞)→ (0,∞), a, b, c and f : [0,∞)→ R are continuous functions. A suitable Green’s function and its estimates are used in this paper.
منابع مشابه
Asymptotic Behaviour of Oscillatory Solutions of a Fourth-order Nonlinear Differential Equation
Asymptotic behaviour of oscillatory solutions of the fourth-order nonlinear differential equation with quasiderivates y[4] + r(t)f(y) = 0 is studied.
متن کاملOscillatory and Asymptotic Behavior of Fourth Order Nonlinear Neutral Delay Differential Equations with Positive and Negative Coefficients
In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t− τ))′′)′′ + q(t)G(y(t− α)) − h(t)H(y(t− β)) = 0 and (NH) (r(t)(y(t) + p(t)y(t− τ))′′)′′ + q(t)G(y(t− α)) − h(t)H(y(t− β)) = f(t) are studied under the assumption ∫ ∞
متن کاملASYMPTOTIC BEHAVIOUR OF OSCILLATORY SOLUTIONS OF n - TH ORDER DIFFERENTIAL EQUATIONS
In this paper, sufficient conditions have been obtained so that all oscillatory solutions of the n-th order differential equations with quasi derivatives tend to zero as t tends to infinity.
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملAsymptotic problems for fourth-order nonlinear differential equations
By a solution of () we mean a function x ∈ C[Tx,∞), Tx ≥ , which satisfies () on [Tx,∞). A solution is said to be nonoscillatory if x(t) = for large t; otherwise, it is said to be oscillatory. Observe that if λ≥ , according to [, Theorem .], all nontrivial solutions of () satisfy sup{|x(t)| : t ≥ T} > for T ≥ Tx, on the contrary to the case λ < , when nontrivial solutions satisfy...
متن کامل