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SINGULAR PERTURBATION FOR A CLASS OF SEMILINEAR SECOND ORDER SYSTEMS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR
Chang K. W., Lin Zongchi
Acta mathematica scientia,Series B. 1985, 5 (2):
233-241.
We study the boundary value problem εy"=f(t,y,ε,μ),μ < t < 1-μ,y(t,ε,μ)|t=μ=A(ε,μ),y(t,ε,μ)|t=1-μ=B(ε,μ), where ε, μ are two positive parameters,y, f, A, B are n-dimensional vector functions and the boundary is perturbed. This vector boundary problem does not appear to have been studied. Under appropriate assumptions we obtain existence of solution and satisfies |yi(t,e,μ)-Ym(t,ε,μ)| ≤ Li(t,ε,μ)+R4(t,ε,μ)+Γi(ε,μ) where i=1, 2, …, n.
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