On Bounded Positive Stationary Solutions for a Nonlocal Fisher-KPP Equation
نویسندگان
چکیده
We study the existence of stationary solutions for a nonlocal version of the FisherKolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation is a recent study by Berestycki et al. [Nonlinearity 22 (2009), pp. 2813–2844] where the nonlocal FKPP equation has been studied and it was shown for the spatial domain R and sufficiently small nonlocality that there are only two bounded non-negative stationary solutions. Here we generalize this result to Rd using a different approach. In particular, an abstract perturbation argument is used in suitable weighted Sobolev spaces. One aim of the alternative strategy is that it can eventually be generalized to obtain persistence results for hyperbolic invariant sets for other nonlocal evolution equations on unbounded domains with small nonlocality.
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