Existence results of infinitely many weak solutions of a singular subelliptic system on the Heisenberg group
| Autor: | Heidari S., Razani A. |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Acta Universitatis Sapientiae: Mathematica, Vol 14, Iss 1, Pp 90-103 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2066-7752 2022-0006 |
| DOI: | 10.2478/ausm-2022-0006 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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