Unbounded upper and lower solutions theories are established for the Sturm-Liouville boundary value problem of a second order ordinary differential equation on infinite intervals. By using such techniques and the Schäuder fixed point theorem, the existence of solutions as well as the positive ones is obtained. Nagumo conditions play an important role in the nonlinear term involved in the first-order derivatives. © 2008 Elsevier Ltd. All rights reserved.
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