Abstract
The method of quasilinearization for second order differential equation - x ″ = f ( t , x , x ′ ) , t ∈ [ 0 , 1 ] , with nonlinear nonlocal three-point boundary conditions x ( 0 ) = 0 , x ′ ( 1 ) = g ( x ( η ) ) , 0 < η ⩽ 1 , is developed. A monotone sequence of solutions converging uniformly and rapidly to a unique solution of the problem is obtained.
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