We consider the second order BVP x″ = f (t, x, x′), x′(a) = A, x′(b) = B provided that there exist α and β (lower and upper functions) such that: β′ (α) < A < α′(a) and β′(b) < B < α′ (b). We consider monotone and non-monotone approximations of solutions to the Neumann problem. The results and examples are provided.
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