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