Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations
Abstract In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the solution, we obtain the necessary an...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-06-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01619-9 |
| _version_ | 1818469602739355648 |
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| author | Limei Dai Hongfei Li |
| author_facet | Limei Dai Hongfei Li |
| author_sort | Limei Dai |
| collection | DOAJ |
| description | Abstract In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the solution, we obtain the necessary and sufficient conditions of existence of radial symmetric solutions with asymptotic behavior at infinity. |
| first_indexed | 2024-04-13T21:26:50Z |
| format | Article |
| id | doaj.art-451037fab5bf4c028c5f7f558f7e9e8d |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-13T21:26:50Z |
| publishDate | 2022-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-451037fab5bf4c028c5f7f558f7e9e8d2022-12-22T02:29:18ZengSpringerOpenBoundary Value Problems1687-27702022-06-012022111110.1186/s13661-022-01619-9Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equationsLimei Dai0Hongfei Li1School of Mathematics and Information Science, Weifang UniversityCollege of Mathematics and System Science, Shandong University of Science and TechnologyAbstract In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the solution, we obtain the necessary and sufficient conditions of existence of radial symmetric solutions with asymptotic behavior at infinity.https://doi.org/10.1186/s13661-022-01619-9Hessian equationsExterior Dirichlet problemNecessary and sufficient conditions |
| spellingShingle | Limei Dai Hongfei Li Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations Boundary Value Problems Hessian equations Exterior Dirichlet problem Necessary and sufficient conditions |
| title | Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations |
| title_full | Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations |
| title_fullStr | Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations |
| title_full_unstemmed | Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations |
| title_short | Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations |
| title_sort | necessary and sufficient conditions on the existence of solutions for the exterior dirichlet problem of hessian equations |
| topic | Hessian equations Exterior Dirichlet problem Necessary and sufficient conditions |
| url | https://doi.org/10.1186/s13661-022-01619-9 |
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