Zhixian Yu, Rong Yuan
Abstract:
In this article, we establish the existence and
nonexistence of travelling waves for a lattice non-monotone
integral equation which is an epidemic model. Moreover,
the wave is either convergent to the positive equilibrium
or oscillating on the positive equilibrium at positive infinity,
and has the exponential asymptotic behavior at negative infinity.
For the non-monotone case, the asymptotic speed of propagation
also coincides with the minimal wave speed.
Submitted May 10, 2010. Published July 28, 2010.
Math Subject Classifications: 35C07, 35R09, 34A33.
Key Words: Travelling waves; Schauder's fixed point theorem;
non-monotone integral equation; oscillatory solution.
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Zhixian Yu College of Science University of Shanghai for Science and Technology Shanghai 200093, China email: yuzx@mail.bnu.edu.cn | |
Rong Yuan School of Mathematical Sciences Beijing Normal University Beijing 100875, China email: ryuan@bnu.edu.cn |
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