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In the early 2000’s, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-PiskunovFisher equation ut(t, x) =… (More)

We prove the existence of a continuous family of positive and generally non-monotone travelling fronts in delayed reaction-diffusion equations ut(t, x) = ∆u(t, x) − u(t, x) + g(u(t − h, x)) (∗), when… (More)

This paper concerns the semi-wavefronts (i.e. bounded solutions u = φ(x·ν+ct) > 0, |ν| = 1, satisfying φ(−∞) = 0) to the delayed KPP-Fisher equation ut(t, x) = ∆u(t, x) + u(t, x)(1 − u(t− τ, x)), u ≥… (More)

- Adrian Gomez, Sergei I. Trofimchuk
- J. London Math. Society
- 2014

In this paper, we answer the question about the criteria of existence of monotone travelling fronts u = φ(ν · x+ ct), φ(−∞) = 0, φ(+∞) = κ, for the monostable (and, in general, nonquasi-monotone)… (More)

- Eduardo Liz, Viktor Tkachenko, Sergei I. Trofimchuk
- SIAM J. Math. Analysis
- 2003

We consider scalar delay differential equations x′(t) = −δx(t)+f(t, xt) (∗) with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well-known… (More)

Motivated by the uniqueness problem for monostable semi-wave-fronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the… (More)

This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded… (More)

We establish a discrete version of the celebrated Yorke and Wright 3/2-stability criterion for a family of strongly nonlinear non-autonomous difference equations of the form xn+1 = xn + anfn(xn, . .… (More)