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We construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension $n=4,5$. Such a construction is already available in the literature in dimensions $n\ge… Click to show full abstract
We construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension $n=4,5$. Such a construction is already available in the literature in dimensions $n\ge 6$ (see for instance [8,12,27,29,33]) and not possible in dimension $3$ by [25]. This also provides new patterns for the Lin--Ni [21] problem on closed manifolds and completes results by Br\'ezis and Li [6] about this problem.
Keywords:
positive clusters;
elliptic equation;
clusters smooth;
smooth perturbations;
critical elliptic
Journal Title: Journal of Functional Analysis
Year Published: 2018
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Journal Title: Journal of Functional Analysis
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!