A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment

This paper concerns a diffusive logistic equation with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, in which the variable intrinsic growth rate may be “very negative” in a “suitable large region” (see conditions (H1), (H2), (4.3)). Such a model can be used to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. In the case of higher space dimensions with radial symmetry and when the intrinsic growth rate has a positive lower bound, this problem has been studied by Du, Guo & Peng [11]. They established a spreading–vanishing dichotomy, the sharp criteria for spreading and vanishing and estimate of the asymptotic spreading speed. In the present paper, we show that the above results are retained for our problem.