Averaging Method in Multifrequency Systems with Delay and Nonlocal Conditions

Abstract

The complexity of the research of the problem is the existence of resonances. Resonance condition in point τ ∈ [0, L] is q Xν =1 θ ν(kν, ω(θντ)) = 0, kν ∈ Rm, IkI 6= 0. Averaging in system (1) is carried out on fast variables ϕΘ on the torus Tm. The averaged problem takes the form dx…The existence and uniqueness of solution of the problem and the estimation error k x(τ, ε) − x(τ)k ≤ c1εα, where α = (mq)−1, c1 = const > 0 of averaging method is obtained.