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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/813137 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |