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Non existence result of nontrivial solutions to the equation −∆u = f (u)

Salvador López Martínez 1 Alexis Molino 2
1 Paradyse
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : In this paper we prove the nonexistence of nontrivial solution to −∆u = f (u) in Ω, u = 0 on ∂Ω, being Ω ⊂ R N (N ≥ 1) a bounded domain and f locally Lispchitz with non-positive primitive. As a consequence, we discuss the long-time behavior of solutions to the so-called sine-Gordon equation.
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Submitted on : Friday, October 16, 2020 - 7:20:24 PM
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Salvador López Martínez, Alexis Molino. Non existence result of nontrivial solutions to the equation −∆u = f (u). Complex Variables and Elliptic Equations, Taylor & Francis, In press. ⟨hal-02969790⟩

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