We consider the following critical weakly coupled elliptic system -Δui=μi|ui|2-2ui+j≠iβij|uj|22|ui|2-42uiinΩϵui=0on∂Ωϵ,i=1,m,in a domain Ωϵ⊂ℝN, N=3,4, with small shrinking holes as the parameter ϵ→0. We prove the existence of positive solutions of two different types: either each density concentrates around a different hole, or we have groups of components such that all the components within a single group concentrate around the same point, and different groups concentrate around different points.
On Coron's problem for weakly coupled elliptic systems / Pistoia, A.; Soave, N.. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - 116:1(2018), pp. 33-67. [10.1112/plms.12073]
On Coron's problem for weakly coupled elliptic systems
Pistoia A.;Soave N.
2018
Abstract
We consider the following critical weakly coupled elliptic system -Δui=μi|ui|2-2ui+j≠iβij|uj|22|ui|2-42uiinΩϵui=0on∂Ωϵ,i=1,m,in a domain Ωϵ⊂ℝN, N=3,4, with small shrinking holes as the parameter ϵ→0. We prove the existence of positive solutions of two different types: either each density concentrates around a different hole, or we have groups of components such that all the components within a single group concentrate around the same point, and different groups concentrate around different points.| File | Dimensione | Formato | |
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