Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations
We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form 𝑦+𝑝(𝑥)𝑦+𝑞(𝑥)𝑦=𝑓(𝑥), with condition that there exists a nonzero 𝑦1∶𝐼→𝑋 in 𝐶2(𝐼) such that 𝑦1+𝑝(𝑥)𝑦1+𝑞(𝑥)𝑦1=0 and 𝐼 is an open interval. As a consequence of our main theorem, we prove the gene...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/813137 |
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| author | A. Javadian E. Sorouri G. H. Kim M. Eshaghi Gordji |
| author_facet | A. Javadian E. Sorouri G. H. Kim M. Eshaghi Gordji |
| author_sort | A. Javadian |
| collection | DOAJ |
| description | We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential
equation of the form 𝑦+𝑝(𝑥)𝑦+𝑞(𝑥)𝑦=𝑓(𝑥), with condition that there exists a nonzero 𝑦1∶𝐼→𝑋 in 𝐶2(𝐼) such that 𝑦1+𝑝(𝑥)𝑦1+𝑞(𝑥)𝑦1=0 and 𝐼 is an open
interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam
stability of several important well-known differential equations. |
| format | Article |
| id | doaj-art-95753d631bb64db3b0bc4ad8a4d27d53 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-95753d631bb64db3b0bc4ad8a4d27d532025-08-20T03:37:02ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/813137813137Generalized Hyers-Ulam Stability of the Second-Order Linear Differential EquationsA. Javadian0E. Sorouri1G. H. Kim2M. Eshaghi Gordji3Department of Physics, Semnan University, P. O. Box 35195-363, Semnan, IranDepartment of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, IranDepartment of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of KoreaDepartment of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, IranWe prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form 𝑦+𝑝(𝑥)𝑦+𝑞(𝑥)𝑦=𝑓(𝑥), with condition that there exists a nonzero 𝑦1∶𝐼→𝑋 in 𝐶2(𝐼) such that 𝑦1+𝑝(𝑥)𝑦1+𝑞(𝑥)𝑦1=0 and 𝐼 is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.http://dx.doi.org/10.1155/2011/813137 |
| spellingShingle | A. Javadian E. Sorouri G. H. Kim M. Eshaghi Gordji Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations Journal of Applied Mathematics |
| title | Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations |
| title_full | Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations |
| title_fullStr | Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations |
| title_full_unstemmed | Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations |
| title_short | Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations |
| title_sort | generalized hyers ulam stability of the second order linear differential equations |
| url | http://dx.doi.org/10.1155/2011/813137 |
| work_keys_str_mv | AT ajavadian generalizedhyersulamstabilityofthesecondorderlineardifferentialequations AT esorouri generalizedhyersulamstabilityofthesecondorderlineardifferentialequations AT ghkim generalizedhyersulamstabilityofthesecondorderlineardifferentialequations AT meshaghigordji generalizedhyersulamstabilityofthesecondorderlineardifferentialequations |