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, ANGELA;Soave, Nicola
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.
35J15; 35J20; 35J50 (primary); Mathematics (all)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1052439
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