Nonexistence and boundary behavior of solutions to the [formula omitted]-Hessian equation with nonlinear gradient terms.
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| Title: | Nonexistence and boundary behavior of solutions to the [formula omitted]-Hessian equation with nonlinear gradient terms. |
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| Authors: | Zhao, Boxuan1 (AUTHOR) hj19990623@163.com, Wang, Guotao1 (AUTHOR) wanggt@sxnu.edu.cn |
| Source: | Applied Mathematics Letters. Apr2026, Vol. 175, pN.PAG-N.PAG. 1p. |
| Subjects: | Convex domains, Hessian matrices, Equations, Variational approach (Mathematics), Mathematical singularities |
| Abstract: | This paper investigates the blow-up problem for the k -Hessian equation with nonlinear gradient terms: (γ + | D u |) k (p − 2) S k (D 2 u) = h (z) u α (ln u) β > 0 , z ∈ D , u | ∂ D = + ∞ , where p ≥ 2 , α , β , γ are nonnegative constants with β ≠ 0 , D ⊂ R N (N ≥ 2) is a smooth, bounded and strictly (k − 1) -convex domain, h ∈ C ∞ (D) is a positive function and may be singular near ∂ D. By the sub-supersolution method, we present the boundary behavior of large solutions to this problem. Our work essentially generalizes the relevant conclusions in Zhang and Feng (2018); Feng and Zhang (2020). [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics Letters is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 190695160 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Nonexistence and boundary behavior of solutions to the [formula omitted]-Hessian equation with nonlinear gradient terms. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhao%2C+Boxuan%22">Zhao, Boxuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hj19990623@163.com</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Guotao%22">Wang, Guotao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wanggt@sxnu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+Letters%22">Applied Mathematics Letters</searchLink>. Apr2026, Vol. 175, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Convex+domains%22">Convex domains</searchLink><br /><searchLink fieldCode="DE" term="%22Hessian+matrices%22">Hessian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+approach+%28Mathematics%29%22">Variational approach (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates the blow-up problem for the k -Hessian equation with nonlinear gradient terms: (γ + | D u |) k (p − 2) S k (D 2 u) = h (z) u α (ln u) β > 0 , z ∈ D , u | ∂ D = + ∞ , where p ≥ 2 , α , β , γ are nonnegative constants with β ≠ 0 , D ⊂ R N (N ≥ 2) is a smooth, bounded and strictly (k − 1) -convex domain, h ∈ C ∞ (D) is a positive function and may be singular near ∂ D. By the sub-supersolution method, we present the boundary behavior of large solutions to this problem. Our work essentially generalizes the relevant conclusions in Zhang and Feng (2018); Feng and Zhang (2020). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics Letters is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.aml.2025.109846 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Convex domains Type: general – SubjectFull: Hessian matrices Type: general – SubjectFull: Equations Type: general – SubjectFull: Variational approach (Mathematics) Type: general – SubjectFull: Mathematical singularities Type: general Titles: – TitleFull: Nonexistence and boundary behavior of solutions to the [formula omitted]-Hessian equation with nonlinear gradient terms. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhao, Boxuan – PersonEntity: Name: NameFull: Wang, Guotao IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 08939659 Numbering: – Type: volume Value: 175 Titles: – TitleFull: Applied Mathematics Letters Type: main |
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