Existence and uniqueness theorems for a third-order generalized boundary value problem

Chaitan P. Gupta

International Journal of Stochastic Analysis, 1989, vol. 2, 1-19

Abstract:

Let f : [ 0 , 1 ] × ℝ 3 → ℝ be a function satisfying Caratheodory's conditions, e ( x ) ∈ L 1 [ 0 , 1 ] , η ∈ [ 0 , 1 ] , h ≥ 0 , k ≥ 0 , h + k > 0 . This paper studies existence and uniqueness questions for the third-order three-point generalized boundary value problem u ‴ + f ( x , u , u ′ , u ″ ) = e ( x ) , 0 < x < 1 , u ( η ) = 0 , u ″ ( 0 ) − h u ′ ( 0 ) = u ″ ( 1 ) + k u ′ ( 1 ) = 0 , and the associated special cases corresponding to one or both of h and k equal to infinity. The conditions on the nonlinearity f turn out to be related to the spectrum of the linear boundary value problem u ‴ = λ u ′ , u ( η ) = 0 , u ″ ( 0 ) − h u ′ ( 0 ) = u ″ ( 1 ) + k u ′ ( 1 ) = 0 , in a natural way.

Date: 1989
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/2/918359.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/2/918359.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:jnijsa:918359

DOI: 10.1155/S1048953389000031

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().