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math.AP2022
Multi-peak solutions for singularly perturbed nonlinear Dirichlet problems involving critical growth
Yi He, Juncheng Wei, Jianjun Zhang
We consider the following singularly perturbed elliptic problem \[ - {\varepsilon ^2}Δu + u = f(u){\text{ in }}Ω,{\text{ }}u > 0{\text{ in }}Ω,{\text{ }}u = 0{\text{ on }}\partial…
math.AP2019★ 1 cited
Half space theorem for the Allen-Cahn equation and related problems
Francois Hamel, Yong Liu, Pieralberto Sicbaldi +2
In this paper we obtain rigidity results for a bounded non-constant entire solution of the Allen-Cahn equation in , whose level set is contained in a ha…
math.AP2016★ 5 cited
Total masses of solutions to general Toda systems with singular sources
Debabrata Karmakar, Chang-Shou Lin, Zhaohu Nie +1
In this article we obtain total masses of solutions to the Toda system associated to a general simple Lie algebra with singular sources at the origin. The determination of such tot…