Uniqueness for branching diffusion process with absorbing boundary

Abstract

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.

Keywords:

• Uniqueness
• branching diffusion process
• integral equation

2000 Mathematical Subject Classifications:

• 60H15
• 45N05
• 45C05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research supported by NNSF of China [grant number 11871129].