A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation

Zheyan Zhou and Jianhe Shen

Abstract and Applied Analysis, 2010, vol. 2010, 1-20

Abstract:

A second-order boundary value problem with nonlinear and mixed two-point boundary conditions is considered, L x = f ( t , x , x ′ ) , t ∈ ( a , b ) , g ( x ( a ) , x ( b ) , x ′ ( a ) , x ′ ( b ) ) = 0 , x ( b ) = x ( a ) in which L is a formally self-adjoint second-order differential operator. Under appropriate assumptions on L , f , and g , existence and uniqueness of solutions is established by the method of upper and lower solutions and Leray-Schauder degree theory. The general quasilinearization method is then applied to this problem. Two monotone sequences converging quadratically to the unique solution are constructed.

Date: 2010
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2010/287473.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2010/287473.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:287473

DOI: 10.1155/2010/287473

Access Statistics for this article

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