Positive solutions of semilinear problems in an exterior domain of R2 View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-12

AUTHORS

Imed Bachar, Habib Mâagli, Said Mesloub

ABSTRACT

The aim of this paper is to establish the existence and global asymptotic behavior of a positive continuous solution for the following semilinear problem: {−Δu(x)=a(x)uσ(x),x∈D,u>0,in D,u(x)=0,x∈∂D,lim|x|→∞u(x)ln|x|=0, where σ<1, D is an unbounded domain in R2 with a compact nonempty boundary ∂D consisting of finitely many Jordan curves. As main tools, we use Kato class, Karamata regular variation theory and the Schauder fixed point theorem. More... »

PAGES

65

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13661-019-1178-0

DOI

http://dx.doi.org/10.1186/s13661-019-1178-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1113171900


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51 schema:description The aim of this paper is to establish the existence and global asymptotic behavior of a positive continuous solution for the following semilinear problem: {−Δu(x)=a(x)uσ(x),x∈D,u>0,in D,u(x)=0,x∈∂D,lim|x|→∞u(x)ln|x|=0, where σ<1, D is an unbounded domain in R2 with a compact nonempty boundary ∂D consisting of finitely many Jordan curves. As main tools, we use Kato class, Karamata regular variation theory and the Schauder fixed point theorem.
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