Abstract
The upper and lower solutions method and the generalized quasilinearization technique for second order nonlinear m-point boundary value problem of the type - x ″ = f ( t , x , x ′ ) , t ∈ [ 0 , 1 ] δ x ( 0 ) - γ x ′ ( 0 ) = 0 , x ( 1 ) = ∑ i = 1 m - 2 α i x ( η i ) , η i ∈ ( 0 , 1 ) is developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained in the C 1 norm.
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