Positive solutions of a nonlinear Sturm–Liouville boundary-value problem

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AbstractWe establish the existence of positive solutions of the Sturm–Liouville problemwhereWe assume g and $\hat{q}$ to be non-negative, continuous functions, a(s) is a positive continuous function, c≥0, p>1, and the function h is sub-quadratic with respect to u′. We combine a priori estimates with a fixed-point result of Krasnosel'skii to obtain the existence of a positive solution.