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Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland..
Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2019 (English)In: ADVANCES IN NONLINEAR ANALYSIS, ISSN 2191-9496, Vol. 8, no 1, p. 995-1003Article in journal (Refereed) Published
Abstract [en]

We study the semilinear elliptic equation -Delta u = u(alpha)vertical bar log u vertical bar(beta) in B-1 \ {0}, where B-1 subset of R-n, with n >= 3, n/n-2 < alpha <n+2/n-2 and -infinity < beta < infinity. Our main result establishes that the nonnegative solution u is an element of C-2(B-1 \ {0}) of the above equation either has a removable singularity at the origin or it behaves like u(x) = A(1 + o(1))vertical bar x vertical bar(-2/alpha-1)(log 1/vertical bar x vertical bar)(-beta/alpha-1) as x -> 0, with A = [(2/alpha-1)(1-beta)(n - 2 - 2/alpha-1)](1/alpha-1).

Place, publisher, year, edition, pages
WALTER DE GRUYTER GMBH , 2019. Vol. 8, no 1, p. 995-1003
Keywords [en]
Singular solutions, asymptotic behavior, log-type nonlinearity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-246290DOI: 10.1515/anona-2017-0261ISI: 000459891200051Scopus ID: 2-s2.0-85048763020OAI: oai:DiVA.org:kth-246290DiVA, id: diva2:1298939
Note

QC 20190325

Available from: 2019-03-25 Created: 2019-03-25 Last updated: 2019-03-25Bibliographically approved

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Shahgholian, Henrik

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  • apa
  • harvard1
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  • de-DE
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  • nn-NB
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  • Other locale
More languages
Output format
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