Existence of solutions for a family of polyharmonic and biharmonic equations

M. Hesaaraki and B. Raessi

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-13

Abstract:

We consider a family of polyharmonic problems of the form ( − Δ ) m u = g ( x , u ) in Ω , D α u = 0 on ∂ Ω , where Ω ⊂ ℠n is a bounded domain, g ( x , ⋅ ) ∈ L ∞ ( Ω ) , and | α | < m . By using the fibering method, we obtain some results about the existence of solution and its multiplicity under certain assumptions on g . We also consider a family of biharmonic problems of the form Δ 2 u + ( Δ ϕ + | ∇ ϕ | 2 ) Δ u + 2 ∇ ϕ ⋅ ∇ Δ u = g ( x , u ) , where ϕ ∈ C 2 ( Ω ¯ ) , and Ω , g , and the boundary condition are the same as above. For this problem, we prove the existence and multiplicity of solutions too.

Date: 2005
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2005/561415.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2005/561415.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:561415

DOI: 10.1155/IJMMS.2005.3405

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().