## Osaka Journal of Mathematics

### Entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity

#### Abstract

We study entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity. We construct three different types of entire solutions. Each of these entire solutions behaves as two traveling wavefronts connecting two of those three equilibria as time approaches minus infinity. Moreover, the first and second ones are solutions which behave as two traveling wavefronts approaching each other from both sides of $x$-axis. The behavior of the second one is like the first one except it connects two different wavefronts. The third one is a solution which behaves as two different traveling wavefronts and one chases another from the same side of $x$-axis.

#### Article information

Source
Osaka J. Math., Volume 50, Number 3 (2013), 607-629.

Dates
First available in Project Euclid: 27 September 2013

https://projecteuclid.org/euclid.ojm/1380287425

Mathematical Reviews number (MathSciNet)
MR3128995

Zentralblatt MATH identifier
1285.34006

#### Citation

Guo, Jong-Shenq; Lin, Ying-Chin. Entire solutions for a discrete diffusive equation with bistable convolution type nonlinearity. Osaka J. Math. 50 (2013), no. 3, 607--629. https://projecteuclid.org/euclid.ojm/1380287425

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