Positive Solutions for Some Competitive Fractional Systems in Bounded Domains
Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Diric...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/140130 |
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| _version_ | 1832554962537676800 |
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| author | Imed Bachar Habib Mâagli Noureddine Zeddini |
| author_facet | Imed Bachar Habib Mâagli Noureddine Zeddini |
| author_sort | Imed Bachar |
| collection | DOAJ |
| description | Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some
Dirichlet conditions, where 0<α<2, σ,β≥1,s,r≥0. The potential functions p,q are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions Kα(D). |
| format | Article |
| id | doaj-art-69c2fa1e692a4e3ab12f26a9951455ff |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-69c2fa1e692a4e3ab12f26a9951455ff2025-02-03T05:49:57ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/140130140130Positive Solutions for Some Competitive Fractional Systems in Bounded DomainsImed Bachar0Habib Mâagli1Noureddine Zeddini2Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi ArabiaUsing some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Dirichlet conditions, where 0<α<2, σ,β≥1,s,r≥0. The potential functions p,q are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions Kα(D).http://dx.doi.org/10.1155/2013/140130 |
| spellingShingle | Imed Bachar Habib Mâagli Noureddine Zeddini Positive Solutions for Some Competitive Fractional Systems in Bounded Domains Journal of Function Spaces and Applications |
| title | Positive Solutions for Some Competitive Fractional Systems in Bounded Domains |
| title_full | Positive Solutions for Some Competitive Fractional Systems in Bounded Domains |
| title_fullStr | Positive Solutions for Some Competitive Fractional Systems in Bounded Domains |
| title_full_unstemmed | Positive Solutions for Some Competitive Fractional Systems in Bounded Domains |
| title_short | Positive Solutions for Some Competitive Fractional Systems in Bounded Domains |
| title_sort | positive solutions for some competitive fractional systems in bounded domains |
| url | http://dx.doi.org/10.1155/2013/140130 |
| work_keys_str_mv | AT imedbachar positivesolutionsforsomecompetitivefractionalsystemsinboundeddomains AT habibmaagli positivesolutionsforsomecompetitivefractionalsystemsinboundeddomains AT noureddinezeddini positivesolutionsforsomecompetitivefractionalsystemsinboundeddomains |