Abstract
Reaction-diffusion equations with a space dependent nonlinearity are considered on the whole axis. Existence of pulses, stationary solutions which vanish at infinity, is studied by the Leray–Schauder method. It is based on the topological degree for Fredholm and proper operators with the zero index in some special weighted spaces and on a priori estimates of solutions in these spaces. Existence of solutions is related to the speed of travelling wave solutions for the corresponding autonomous equations with the limiting nonlinearity.
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Eymard, N., Volpert, V. & Vougalter, V. Existence of Pulses for Local and Nonlocal Reaction-Diffusion Equations. J Dyn Diff Equat 29, 1145–1158 (2017). https://doi.org/10.1007/s10884-015-9487-1
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DOI: https://doi.org/10.1007/s10884-015-9487-1