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Title: Solvability of a fourth-order boundary value problem with periodic boundary conditions II

Let f : [ 0 , 1 ] × R 4 R be a function satisfying Caratheodory's conditions and e ( x ) L 1 [ 0 , 1 ] . This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d 4 u d x 4 + f ( x , u ( x ) , u ( x ) , u ( x ) , u ( x ) ) = e ( x ) ,    0 < x < 1 , with u ( 0 ) u ( 1 ) = u ( 0 ) u ( 1 ) = u ( 0 ) - u ( 1 ) = u ( 0 ) - u ( 1 ) = 0 . This problem was studied earlier by the author in the special case when f was of the form f ( x , u ( x ) ) , i.e., independent of u ( x ) , u ( x ) , u ( x ) . It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problems d 4 u d x 4 = λ 4 u and d 4 u d x 4 = λ 2 d 2 u d x 2 with periodic boundary conditions.
Authors:
 [1]
  1. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439-4801, USA
Publication Date:
OSTI Identifier:
1198035
Grant/Contract Number:
W-31-109-Eng-38
Type:
Published Article
Journal Name:
International Journal of Mathematics and Mathematical Sciences
Additional Journal Information:
Journal Volume: 14; Journal Issue: 1; Related Information: CHORUS Timestamp: 2016-08-23 12:12:35; Journal ID: ISSN 0161-1712
Publisher:
Hindawi Publishing Corporation
Sponsoring Org:
USDOE
Country of Publication:
Country unknown/Code not available
Language:
English