Existence and uniqueness of analytic solutions of the Shabat equation
Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely for z∈ℂ:|z|<T, T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.855 |
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| _version_ | 1849305613203406848 |
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| author | Eugenia N. Petropoulou |
| author_facet | Eugenia N. Petropoulou |
| author_sort | Eugenia N. Petropoulou |
| collection | DOAJ |
| description | Sufficient conditions are given so that the initial value problem
for the Shabat equation has a unique analytic solution, which,
together with its first derivative, converges absolutely for z∈ℂ:|z|<T, T>0. Moreover, a bound of this solution
is given. The sufficient conditions involve only the initial
condition, the parameters of the equation, and T. Furthermore,
from these conditions, one can obtain an upper bound for T. Our
results are in consistence with some recently found results. |
| format | Article |
| id | doaj-art-045ca3f820bd403d830c610a4db3fe47 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-045ca3f820bd403d830c610a4db3fe472025-08-20T03:55:23ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005885586210.1155/AAA.2005.855Existence and uniqueness of analytic solutions of the Shabat equationEugenia N. Petropoulou0Division of Applied Mathematics and Mechanics, Mechanics, Department of Engineering Sciences, School of Engineering, University of Patras, Patras 26500, GreeceSufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely for z∈ℂ:|z|<T, T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, and T. Furthermore, from these conditions, one can obtain an upper bound for T. Our results are in consistence with some recently found results.http://dx.doi.org/10.1155/AAA.2005.855 |
| spellingShingle | Eugenia N. Petropoulou Existence and uniqueness of analytic solutions of the Shabat equation Abstract and Applied Analysis |
| title | Existence and uniqueness of analytic solutions of the Shabat equation |
| title_full | Existence and uniqueness of analytic solutions of the Shabat equation |
| title_fullStr | Existence and uniqueness of analytic solutions of the Shabat equation |
| title_full_unstemmed | Existence and uniqueness of analytic solutions of the Shabat equation |
| title_short | Existence and uniqueness of analytic solutions of the Shabat equation |
| title_sort | existence and uniqueness of analytic solutions of the shabat equation |
| url | http://dx.doi.org/10.1155/AAA.2005.855 |
| work_keys_str_mv | AT eugenianpetropoulou existenceanduniquenessofanalyticsolutionsoftheshabatequation |