On a generalized population dynamics equation with environmental noise

Abstract We establish the existence and uniqueness of global (in time) positive strong solutions for a generalized population dynamics equation with environmental noise, while fails deterministic equation. Particularly, we prove following stochastic differential d X t = ( θ m 0 + k ) e 1 2 φ W , > ⩾ x ∈ R being constants r ϑ or | log also show that index is sharp in sense if one can choose certain proper such solution will explode finite time almost surely.