Study of Periodic Solutions for a Ninth-Order Non-Autonomous Differential Equation Using First-Order Averaging Theory - Berrehail, Chems Eddine; Bouslah, Zineb (Journal of Applied Nonlinear Dynamics, 2026)
In this paper, we use the averaging theory of first order to study the periodic solutions of the perturbed ninth-order non-autonomous differential equation x^(9)-λ x^8+ψ x^(7)-λ ψ x^(6)+φ.....x-λ χ ....x+A(...x-λ ..x)+p^2 b^2( c^2x-c^2)=ε F where F=F(t,x,.x,..x,...x,....x,x^(5),x^(6),x^(7),x^(8)), ψ=p^2+b^2+c^2+1, φ=p^2c^2+p^2 b^2+b^2c^2+p^2+b^2+c^2, A=p^2b^2+p^2c^2+b^2 c^2+p^2b^2c^2, with b, c and p are rational numbers different from -1, 0, 1, and p eq ± b , p eq ± c , b eq ± c , ε is sufficiently small and F is a nonlinear non-autonomous periodic function. We present some applications to illustrate our main results.