With suitable assumptions, uniqueness of nontrivial nonnegative solution is established for the following nonlinear integral equation $\phi (x)={\int }_{\mathcal{D}}E(x,y)G(y,\phi (y))\mathrm{d}y.$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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具有吸收边界的分支扩散过程的唯一性

在适当的假设下，建立下列非线性积分方程的非平凡非负解的唯一性$\phi (X)={\int }_{\mathcal{D}}乙(X,\mathrm{是的})G(\mathrm{是的},\phi (\mathrm{是的}))\mathrm{d}\mathrm{是的}.$该结果适用于具有吸收边界的分支扩散过程。特别是 Pazy 和 Rabinowitz 研究中存在的一个问题 [A非线性积分方程与中子输运理论的应用。拱口机械肛门。1969;32:226-246] 已解决。