Abstract
With suitable assumptions, uniqueness of nontrivial nonnegative solution is established for the following nonlinear integral equation This result is applied to branching diffusion processes with absorbing boundary. In particular, a question existing in the study by Pazy and Rabinowitz [A nonlinear integral equation with applications to neutron transport theory. Arch Ration Mech Anal. 1969;32:226-246] is solved.
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