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Monotonicity in integrodifferential equations

Abstract : We study the behavior of positive solutions of the Dirichlet problem Lu = f (u) in Ω with Ω = (a,+∞), where a can be −∞, and L is an abstract operator which is non-increasing under translation and satisfies a strong maximum principle property. This covers the case of many integral operators. Under some assumptions on f (e.g., bistable, monostable), we show that any solution exhibits a monotone behavior
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Submitted on : Sunday, May 31, 2020 - 7:19:13 PM
Last modification on : Tuesday, August 18, 2020 - 3:34:03 PM

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Jerome Coville. Monotonicity in integrodifferential equations. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2003, 337 (7), pp.445-450. ⟨10.1016/j.crma.2003.07.005⟩. ⟨hal-02677393⟩

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