(untitled) (Нелінійні коливання, 1999)
The authors consider the multipoint problem with parameters, dx/dτ=a(x,φ,τ,╣),dφ/dτ =ω(τ)/ε+b(x,φ,τ,╣), F(xτ=τ1,…,xτ=τr,φτ=τ 1,…,φτ=τr,╣,ε)=0. Here xRn, φRm, τ[0,L]R, ╣Rs is the parameter, ε(0,ε0], FRn×Rm× Rs×(0,ε0]→R(n+m+s), 0τ1…τrL, r2. The system is averaged with respect to the fast variable φ . The authors prove the solvability of the problem and obtain the estimate x(τ,ε)-y(τ,ε)+φ(τ,ε)- ψ(τ,ε)+╣(ε )-╣0σ εα for all (τ,ε)[0,L]×(0,ε0]. Here y,ψ are the solution of the averaged system, σR, αR.