General existence principles for nonlocal boundary value problems with φ -Laplacian and their applications

Ravi P. Agarwal, Donal O'Regan and Svatoslav Stanek

Abstract and Applied Analysis, 2006, vol. 2006, 1-30

Abstract:

The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form ( φ ( x ′ ) ) ′ = f 1 ( t , x , x ′ ) + f 2 ( t , x , x ′ ) F 1 x + f 3 ( t , x , x ′ ) F 2 x , α ( x ) = 0 , β ( x ) = 0 , where f j satisfy local Carathéodory conditions on some [ 0 , T ] × 𝒟 j ⊂ â„ 2 , f j are either regular or have singularities in their phase variables ( j = 1 , 2 , 3 ) , F i : C 1 [ 0 , T ] → C 0 [ 0 , T ] ( i = 1 , 2 ) , and α , β : C 1 [ 0 , T ] → â„ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.

Date: 2006
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2006/096826.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2006/096826.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:096826

DOI: 10.1155/AAA/2006/96826

Access Statistics for this article

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