Multiplicity Results for p -Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions

Tsing-San Hsu

Abstract and Applied Analysis, 2009, vol. 2009, 1-24

Abstract:

The multiple results of positive solutions for the following quasilinear elliptic equation: − Δ ð ‘ ð ‘¢ = 𠜆 ð ‘“ ( ð ‘¥ ) | ð ‘¢ | ð ‘ž − 2 ð ‘¢ + ð ‘” ( ð ‘¥ ) | ð ‘¢ | ð ‘ âˆ— − 2 ð ‘¢ in Ω , ð ‘¢ = 0 on 𠜕 Ω , are established. Here, 0 ∈ Ω is a bounded smooth domain in â„ ð ‘ , Δ ð ‘ denotes the ð ‘ -Laplacian operator, 1 ≤ ð ‘ž < ð ‘ < ð ‘ , ð ‘ âˆ— = ð ‘ ð ‘ / ( ð ‘ âˆ’ ð ‘ ) , 𠜆 is a positive real parameter, and ð ‘“ , ð ‘” are continuous functions on Ω which are somewhere positive but which may change sign on Ω . The study is based on the extraction of Palais-Smale sequences in the Nehari manifold.

Date: 2009
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2009/652109.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2009/652109.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:jnlaaa:652109

DOI: 10.1155/2009/652109

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().