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Perron theorem in the monotone iteration method for traveling waves in delayed reaction-diffusion equations. (English) Zbl 1154.34031

The existence of monotone traveling waves for delayed reaction-diffusion systems is studied. This class of equations is important on account of its relevance in population dynamics and biology. Based on the construction and differentiability of upper and lower solutions, the authors apply the Perron theorem and thereby set up a rigorous framework for the monotone iteration method. As an outcome the existence of monotone traveling waves follows. Finally, the authors apply their results for a predator-prey model and the Belousov-Zhabotinskii model with delay.

MSC:

34K10 Boundary value problems for functional-differential equations
35R10 Partial functional-differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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