A Two-Point Boundary Value Problem with Reflection of the Argument
We consider the following two-point boundary value problems u″x+uπ−x+gx,uπ−x=hx in 0,π,u0=0=uπ, and u″x+uπ−x−gx,uπ−x=−hx in 0,π,u0=0=uπ, by setting h∈L10,π and g:0,π×R⟶R being a Caratheodory function. When a,b∈L10,π, ax≤3 for x∈0,π a.e. with strict inequality on a positive measurable subset of 0,π,...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/6010530 |
| _version_ | 1797403739551694848 |
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| author | Nai-Sher Yeh |
| author_facet | Nai-Sher Yeh |
| author_sort | Nai-Sher Yeh |
| collection | DOAJ |
| description | We consider the following two-point boundary value problems u″x+uπ−x+gx,uπ−x=hx in 0,π,u0=0=uπ, and u″x+uπ−x−gx,uπ−x=−hx in 0,π,u0=0=uπ, by setting h∈L10,π and g:0,π×R⟶R being a Caratheodory function. When a,b∈L10,π, ax≤3 for x∈0,π a.e. with strict inequality on a positive measurable subset of 0,π, and gx,u≤axu+bx for x∈0,π a.e. as well as sufficiently large u, several existence theorems will be obtained, with or without a sign condition. |
| first_indexed | 2024-03-09T02:43:45Z |
| format | Article |
| id | doaj.art-e28510b1cd1444c99a51970ff6543513 |
| institution | Directory Open Access Journal |
| issn | 2314-8888 |
| language | English |
| last_indexed | 2024-03-09T02:43:45Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj.art-e28510b1cd1444c99a51970ff65435132023-12-06T00:00:01ZengHindawi LimitedJournal of Function Spaces2314-88882023-01-01202310.1155/2023/6010530A Two-Point Boundary Value Problem with Reflection of the ArgumentNai-Sher Yeh0Department of MathematicsWe consider the following two-point boundary value problems u″x+uπ−x+gx,uπ−x=hx in 0,π,u0=0=uπ, and u″x+uπ−x−gx,uπ−x=−hx in 0,π,u0=0=uπ, by setting h∈L10,π and g:0,π×R⟶R being a Caratheodory function. When a,b∈L10,π, ax≤3 for x∈0,π a.e. with strict inequality on a positive measurable subset of 0,π, and gx,u≤axu+bx for x∈0,π a.e. as well as sufficiently large u, several existence theorems will be obtained, with or without a sign condition.http://dx.doi.org/10.1155/2023/6010530 |
| spellingShingle | Nai-Sher Yeh A Two-Point Boundary Value Problem with Reflection of the Argument Journal of Function Spaces |
| title | A Two-Point Boundary Value Problem with Reflection of the Argument |
| title_full | A Two-Point Boundary Value Problem with Reflection of the Argument |
| title_fullStr | A Two-Point Boundary Value Problem with Reflection of the Argument |
| title_full_unstemmed | A Two-Point Boundary Value Problem with Reflection of the Argument |
| title_short | A Two-Point Boundary Value Problem with Reflection of the Argument |
| title_sort | two point boundary value problem with reflection of the argument |
| url | http://dx.doi.org/10.1155/2023/6010530 |
| work_keys_str_mv | AT naisheryeh atwopointboundaryvalueproblemwithreflectionoftheargument AT naisheryeh twopointboundaryvalueproblemwithreflectionoftheargument |