# American Institute of Mathematical Sciences

March  2016, 15(2): 319-334. doi: 10.3934/cpaa.2016.15.319

## Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

 1 School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000 2 Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

Received  October 2014 Revised  October 2015 Published  January 2016

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.
Citation: Guo Lin, Haiyan Wang. Traveling wave solutions of a reaction-diffusion equation with state-dependent delay. Communications on Pure & Applied Analysis, 2016, 15 (2) : 319-334. doi: 10.3934/cpaa.2016.15.319
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