Solvability of a fourth-order boundary value problem with periodic boundary conditions II
Let f:[0,1]×R4→R be a function satisfying Caratheodory's conditions and e(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d4udx4+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‴...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000121 |
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| author | Chaitan P. Gupta |
| author_facet | Chaitan P. Gupta |
| author_sort | Chaitan P. Gupta |
| collection | DOAJ |
| description | Let f:[0,1]×R4→R be a function satisfying Caratheodory's conditions and
e(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary
value problem
d4udx4+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
d4udx4=λ4u and d4udx4=−λ2d2udx2 with periodic boundary conditions. |
| format | Article |
| id | doaj-art-8b4dac955f6b402e927bb2cb1cc3b027 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8b4dac955f6b402e927bb2cb1cc3b0272025-08-20T02:09:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114112713710.1155/S0161171291000121Solvability of a fourth-order boundary value problem with periodic boundary conditions IIChaitan P. Gupta0Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439-4801, USALet f:[0,1]×R4→R be a function satisfying Caratheodory's conditions and e(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d4udx4+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 d4udx4=λ4u and d4udx4=−λ2d2udx2 with periodic boundary conditions.http://dx.doi.org/10.1155/S0161171291000121 |
| spellingShingle | Chaitan P. Gupta Solvability of a fourth-order boundary value problem with periodic boundary conditions II International Journal of Mathematics and Mathematical Sciences |
| title | Solvability of a fourth-order boundary value problem with periodic boundary conditions II |
| title_full | Solvability of a fourth-order boundary value problem with periodic boundary conditions II |
| title_fullStr | Solvability of a fourth-order boundary value problem with periodic boundary conditions II |
| title_full_unstemmed | Solvability of a fourth-order boundary value problem with periodic boundary conditions II |
| title_short | Solvability of a fourth-order boundary value problem with periodic boundary conditions II |
| title_sort | solvability of a fourth order boundary value problem with periodic boundary conditions ii |
| url | http://dx.doi.org/10.1155/S0161171291000121 |
| work_keys_str_mv | AT chaitanpgupta solvabilityofafourthorderboundaryvalueproblemwithperiodicboundaryconditionsii |