The existence of positive solutions for an elliptic boundary value problem

G. A. Afrouzi

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-6

Abstract:

By using the mountain pass lemma, we study the existence of positive solutions for the equation − Δ u ( x ) = λ ( u | u | + u ) ( x ) for x ∈ Ω together with Dirichlet boundary conditions and show that for every λ < λ 1 , where λ 1 is the first eigenvalue of − Δ u = λ u in Ω with the Dirichlet boundary conditions, the equation has a positive solution while no positive solution exists for λ ≥ λ 1 .

Date: 2005
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2005/263684.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2005/263684.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:263684

DOI: 10.1155/IJMMS.2005.2005

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 ().