2016
DOI: 10.1007/s00526-016-1091-7
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On elliptic systems with Sobolev critical growth

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Cited by 60 publications
(61 citation statements)
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“…In [24], the first author and A. Pistoia constructed, via a Lyapunov-Schmidt reduction and under appropriate assumptions on the domain Ω ⊂ R 4 , families of positive solutions of (1) in the competitive or weakly cooperative cases with all the components u i blowing up at different points as λ i → 0 − . In [9,13,21], the authors investigated the existence and multiplicity of fully nontrivial solutions to (1) with λ i = 0 for the critical case in R N . Recently [23,24] are concerned with existence and concentration results for a Coron-type problem in a bounded domain with one or multiple small holes in the case λ i = 0.…”
Section: Introductionmentioning
confidence: 99%
“…In [24], the first author and A. Pistoia constructed, via a Lyapunov-Schmidt reduction and under appropriate assumptions on the domain Ω ⊂ R 4 , families of positive solutions of (1) in the competitive or weakly cooperative cases with all the components u i blowing up at different points as λ i → 0 − . In [9,13,21], the authors investigated the existence and multiplicity of fully nontrivial solutions to (1) with λ i = 0 for the critical case in R N . Recently [23,24] are concerned with existence and concentration results for a Coron-type problem in a bounded domain with one or multiple small holes in the case λ i = 0.…”
Section: Introductionmentioning
confidence: 99%
“…It is worth to mention that the more general Pohozaev to the general elliptic equations in a non-star-shaped bounded domain can help us to obtain the necessary conditions of the existence of solutions for some special equations. See [21][22][23][24][25][26][27]. In [27], Peng, Peng, and Wang discussed in detail the existence and the form of positive solution, the uniqueness of the minimal energy solution of system (1.11) when p = 2.…”
Section: Introductionmentioning
confidence: 99%
“…In the past decades, the Laplacian equation or system has been widely investigated and there are many results about ground state solutions, multiple positive solutions, signchanging solutions, etc(see [30,31,11,13,14,12,15] and references therein).…”
Section: Introductionmentioning
confidence: 99%