# Non existence result of nontrivial solutions to the equation - $\Delta u = f(u)$

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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https://hal.inria.fr/hal-02969790
Contributor : Salvador López Martínez Connect in order to contact the contributor
Submitted on : Friday, October 16, 2020 - 7:20:24 PM
Last modification on : Thursday, February 11, 2021 - 2:06:47 PM
Long-term archiving on: : Sunday, January 17, 2021 - 11:36:50 PM

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Salvador López Martínez, Alexis Molino. Non existence result of nontrivial solutions to the equation - $\Delta u = f(u)$. Complex Variables and Elliptic Equations, Taylor & Francis, 2020, ⟨10.1080/17476933.2020.1825397⟩. ⟨hal-02969790⟩

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