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Existence of pulses for local and nonlocal reaction-diffusion equations. (English) Zbl 1373.35169

Summary: 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.

MSC:

35K57 Reaction-diffusion equations
35A16 Topological and monotonicity methods applied to PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D15 Problems related to evolution
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