Existence and Uniqueness for a Stochastic Age-dependent Population System with Diffusion Under non-Lipschitz Condition

摘要

In this paper, we study a class of stochastic agedependent population dynamic system with diffusion, which coefficient is non-Lipschitzian with respect to the population density P. By successive approximation of solutions in a general functional setting, using the Bihari inequality and the Davis inequality, we prove the existence and uniqueness of solutions for a stochastic age-dependent population dynamic system in Hilbert space.