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Ground states of critical and supercritical problems of Brezis-Nirenberg type
Stockholm University, Faculty of Science, Department of Mathematics.
2016 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 5, 1787-1802 p.Article in journal (Refereed) Published
Abstract [en]

We study the existence of symmetric ground states to the supercritical problem -Delta v = lambda v + vertical bar v vertical bar(p-2) v in Omega, v = 0 on partial derivative Omega in a domain of the form Omega = {( y, z) is an element of Rk+ 1 x RN- k-1 : (vertical bar y vertical bar, z) is an element of Theta}, where Theta is a bounded smooth domain such that (Theta) over bar subset of (0,infinity) x RN-k-1, 1 <= k <= N - 3, lambda is an element of R, and p = 2(N-k)/N-k-2 is the (k + 1)-st critical exponent. We show that symmetric ground states exist for. in some interval to the left of each symmetric eigenvalue and that no symmetric ground states exist in some interval (-infinity, lambda(*)) with lambda(*) > 0 if k >= 2. Related to this question is the existence of ground states to the anisotropic critical problem -div(a(x)del u) = lambda b(x) u + c(x) vertical bar u vertical bar(2*-2) u in Theta, u = 0 on partial derivative Theta, where a, b, c are positive continuous functions on (Theta) over bar. We give a minimax characterization for the ground states of this problem, study the ground state energy level as a function of., and obtain a bifurcation result for ground states.

Place, publisher, year, edition, pages
2016. Vol. 195, no 5, 1787-1802 p.
Keyword [en]
Supercritical elliptic problem, anisotropic critical problem, ground states, bifurcation
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-123546DOI: 10.1007/s10231-015-0548-1ISI: 000382005400020OAI: oai:DiVA.org:su-123546DiVA: diva2:874654
Available from: 2015-11-27 Created: 2015-11-27 Last updated: 2016-11-25Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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