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Journal Articles Complex Variables and Elliptic Equations Year : 2020

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

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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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Dates and versions

hal-02969790 , version 1 (16-10-2020)

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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, 2020, ⟨10.1080/17476933.2020.1825397⟩. ⟨hal-02969790⟩
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