Traveling wave solutions in n-dimensional delayed reaction-diffusion systems with mixed monotonicity

• Autores: Yuan Lin, Qi-Ru Wang, Kai Zhou
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 243, Nº 1, 2013, págs. 16-27
• Idioma: inglés
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• Resumen

  • This paper deals with the existence of traveling wave solutions for n-components delayed reaction�diffusion systems with mixed monotonicity. Based on a certain kind of mixedquasimonotonicity reaction terms of higher dimension, we propose new conditions on the reaction terms and new definitions of upper and lower solutions. By using Schauder�s fixed point theorem and a cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained will be applied to type-K monotone diffusive Lotka�Volterra systems of higher dimension.