Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group
This article shows the existence and multiplicity of weak solutions for the singular subelliptic system on the Heisenberg group {-Δℍnu+a(ξ)u(|z|4+t2)12=λFu(ξ,u,v)in Ω,-Δℍnv+b(ξ)v(|z|4+t2)12=λFv(ξ,u,v)in Ω,u=v=0on ∂Ω.\left\{ {\matrix{ { - {\Delta _{{\mathbb{H}^n}}}u + a\left( \xi \right){u \o...
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| Format: | Article |
| Language: | English |
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Sciendo
2022-11-01
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| Series: | Acta Universitatis Sapientiae: Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/ausm-2022-0006 |
| _version_ | 1811171451153154048 |
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| author | Heidari S. Razani A. |
| author_facet | Heidari S. Razani A. |
| author_sort | Heidari S. |
| collection | DOAJ |
| description | This article shows the existence and multiplicity of weak solutions for the singular subelliptic system on the Heisenberg group
{-Δℍnu+a(ξ)u(|z|4+t2)12=λFu(ξ,u,v)in Ω,-Δℍnv+b(ξ)v(|z|4+t2)12=λFv(ξ,u,v)in Ω,u=v=0on ∂Ω.\left\{ {\matrix{ { - {\Delta _{{\mathbb{H}^n}}}u + a\left( \xi \right){u \over {{{\left( {{{\left| z \right|}^4} + {t^2}} \right)}^{{1 \over 2}}}}} = \lambda {F_u}\left( {\xi ,u,v} \right)} \hfill & {in\,\,\,\Omega ,} \hfill \cr { - {\Delta _{{\mathbb{H}^n}}}v + b\left( \xi \right){v \over {{{\left( {{{\left| z \right|}^4} + {t^2}} \right)}^{{1 \over 2}}}}} = \lambda {F_v}\left( {\xi ,u,v} \right)} \hfill & {in\,\,\,\Omega ,} \hfill \cr {u = v = 0} \hfill & {on\,\,\partial \Omega .} \hfill \cr } } \right.
The approach is based on variational methods. |
| first_indexed | 2024-04-10T17:15:27Z |
| format | Article |
| id | doaj.art-b94161d9d5884da3b17ec124d2c201ed |
| institution | Directory Open Access Journal |
| issn | 2066-7752 |
| language | English |
| last_indexed | 2024-04-10T17:15:27Z |
| publishDate | 2022-11-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Acta Universitatis Sapientiae: Mathematica |
| spelling | doaj.art-b94161d9d5884da3b17ec124d2c201ed2023-02-05T17:56:42ZengSciendoActa Universitatis Sapientiae: Mathematica2066-77522022-11-011419010310.2478/ausm-2022-0006Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg groupHeidari S.0Razani A.1Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, P. O. Box 34149-16818, Qazvin, IranDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, P. O. Box 34149-16818, Qazvin, IranThis article shows the existence and multiplicity of weak solutions for the singular subelliptic system on the Heisenberg group {-Δℍnu+a(ξ)u(|z|4+t2)12=λFu(ξ,u,v)in Ω,-Δℍnv+b(ξ)v(|z|4+t2)12=λFv(ξ,u,v)in Ω,u=v=0on ∂Ω.\left\{ {\matrix{ { - {\Delta _{{\mathbb{H}^n}}}u + a\left( \xi \right){u \over {{{\left( {{{\left| z \right|}^4} + {t^2}} \right)}^{{1 \over 2}}}}} = \lambda {F_u}\left( {\xi ,u,v} \right)} \hfill & {in\,\,\,\Omega ,} \hfill \cr { - {\Delta _{{\mathbb{H}^n}}}v + b\left( \xi \right){v \over {{{\left( {{{\left| z \right|}^4} + {t^2}} \right)}^{{1 \over 2}}}}} = \lambda {F_v}\left( {\xi ,u,v} \right)} \hfill & {in\,\,\,\Omega ,} \hfill \cr {u = v = 0} \hfill & {on\,\,\partial \Omega .} \hfill \cr } } \right. The approach is based on variational methods.https://doi.org/10.2478/ausm-2022-0006singular potentialvariational methodsinfinitely many solutionsheisenberg group35r0335j2035j1558e3035j61 |
| spellingShingle | Heidari S. Razani A. Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group Acta Universitatis Sapientiae: Mathematica singular potential variational methods infinitely many solutions heisenberg group 35r03 35j20 35j15 58e30 35j61 |
| title | Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group |
| title_full | Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group |
| title_fullStr | Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group |
| title_full_unstemmed | Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group |
| title_short | Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group |
| title_sort | existence results of infinitely many weak solutions of a singular subelliptic system on the heisenberg group |
| topic | singular potential variational methods infinitely many solutions heisenberg group 35r03 35j20 35j15 58e30 35j61 |
| url | https://doi.org/10.2478/ausm-2022-0006 |
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