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Nonexistence result of nontrivial solutions to the equation −Δu=f(u)
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2020-12-21 , DOI: 10.1080/17476933.2020.1825397
Salvador López-Martínez 1 , Alexis Molino 2
Affiliation  

In this paper we prove the nonexistence of nontrivial solutions to Δu=f(u)in Ω,u=0on Ω, with ΩRN (N1) a bounded domain and f locally Lispchitz with nonpositive primitive. As a consequence, we discuss the long-time behavior of solutions to the so-called sine-Gordon equation.



中文翻译:

方程 -Δu=f(u) 的非平凡解的不存在结果

在本文中,我们证明了非平凡解的不存在性-Δ=F()在 Ω,=0在 Ω,ΩRñ(ñ1) 一个有界域和f局部 Lispchitz 与非正原语。因此,我们讨论了所谓的正弦-戈登方程解的长期行为。

更新日期:2020-12-21
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