Existence of Stationary Pulses for Nonlocal Reaction-Diffusion Equations

A nonlocal reaction-diffusion equation and a system of equations from population dynamics are considered on the whole axis. Existence of solutions in the form of stationary pulses is proved by a perturbation method. It is based on spectral properties of the linearized operators and on the implicit function theorem.

2010 Mathematics Subject Classification: 35K57, 35A16, 92D15

Keywords and Phrases: reaction-diffusion equation, existence of pulse solutions, perturbation methods

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