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Nathalie Eymard, Vitaly Volpert, Vitali Vougalter
Existence of pulses for local and nonlocal reaction-diffusion equations
ABSTRACT. Reaction-diffusion equations with 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.