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In this paper, a comparison result for (k, n − k) conjugate boundary value problems is established. By using the monotone iterative technique and the method of upper and lower solutions, we investigate the existence of extremal solutions for a nonlinear differential equation with (k, n− k) conjugate boundary value problems. As an application, an example is presented to illustrate the main results.

Monotone iterative technique for $(k, n-k)$ conjugate boundary value problems