Zongming Guo

TL;DR: In this paper, a diffusive logistic equation with a free boundary in higher space dimensions and a heterogeneous environment was studied, and the spreading-vanishing dichotomy established in Du and Lin (2010) [10] still holds in the more general and ecologically realistic setting considered here.

TL;DR: In this paper, the authors study the diffusive logistic equation with a free boundary in time-periodic environment and show that the spreading-vanishing dichotomy is retained in time periodic environment, and also determine the spreading speed.

TL;DR: In this paper, the authors considered the Fisher-KPP problem with a free boundary governed by a one-phase Stefan condition, and established the existence and uniqueness of the weak solution, and through suitable comparison arguments, extended some of the results obtained earlier in Du and Lin (2010) [11] and Du and Guo (2011) to this general case.

TL;DR: In this article, the authors studied the behavior of finite Morse index solutions of the equation − Δ u = | x | α | u | p − 1 u in Ω ⊂ R N, where p > 1, α > − 2, and Ω is a bounded or unbounded domain.

TL;DR: In this paper, the authors discuss the existence, uniqueness and asymptotic behaviour of various boundary blow-up solutions for a class of quasilinear elliptic equations, which are then used to obtain a rather complete understanding of some quasILinear problems on a bounded domain or over the entire R N N.