The forward and non-forward Amati-Bertocchi-Fubini-Stanghellini-Tonin (ABFST) multiperipheral integral equations with pion exchange and resonance production are solved in a factorizable approximation to the kernel. The solution, which determines the Regge trajectories, is continuous at t = 0 and is analytically continued and studied for all t. In this pion exchange model, the slope of the pomeron trajectory at t = 0 is calculated and is found to have a crucial dependence on the pion mass. The

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... Tr cross section is also calculated in this approximation. The behavior of the trajectories near threshold is shown to be the same as in potential theory. The t ~ + oo limits of the solution are also analyzed.