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By using the fixed-point index theory in a cone and defining a linear operator, we obtain the existence of at least one positive solution for the third-order boundary value problem with integral boundary conditions (Equation presented) where f: [0, 1] × R + × R - → R + is a nonnegative function. The associated Green's function for the above problem is also used, and a new reproducing cone also used. © 2012 Guo et al; licensee Springer.

Positive solutions for the third-order boundary value problems with the second derivatives