Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type
This paper is concerned with the existence of mild and strong solutions on the interval for some neutral partial differential equations with nonlocal conditions. The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear p...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/503656 |
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| _version_ | 1832548488883208192 |
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| author | Hsiang Liu Cheng-Wen Liao Chin-Tzong Pang |
| author_facet | Hsiang Liu Cheng-Wen Liao Chin-Tzong Pang |
| author_sort | Hsiang Liu |
| collection | DOAJ |
| description | This paper is concerned with the existence of mild and strong solutions on
the interval for some neutral partial differential
equations with nonlocal conditions. The linear part of the
equations is assumed to generate a compact analytic semigroup of
bounded linear operators, whereas the nonlinear part satisfies the
Carathëodory condition and is bounded by some suitable
functions. We first employ the Schauder fixed-point theorem to prove
the existence of solution on the interval for
that is small enough, and, then, by letting and using a diagonal argument, we have the existence results on
the interval . This approach allows one to drop the
compactness assumption on a nonlocal condition, which generalizes
recent conclusions on this topic. The obtained results will be
applied to a class of functional partial differential equations with nonlocal conditions. |
| format | Article |
| id | doaj-art-bda58402353e4c1eb79f9012d434066b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bda58402353e4c1eb79f9012d434066b2025-02-03T06:14:03ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/503656503656Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral TypeHsiang Liu0Cheng-Wen Liao1Chin-Tzong Pang2Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Taoyuan 320, TaiwanDepartment of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Taoyuan 320, TaiwanDepartment of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Taoyuan 320, TaiwanThis paper is concerned with the existence of mild and strong solutions on the interval for some neutral partial differential equations with nonlocal conditions. The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear part satisfies the Carathëodory condition and is bounded by some suitable functions. We first employ the Schauder fixed-point theorem to prove the existence of solution on the interval for that is small enough, and, then, by letting and using a diagonal argument, we have the existence results on the interval . This approach allows one to drop the compactness assumption on a nonlocal condition, which generalizes recent conclusions on this topic. The obtained results will be applied to a class of functional partial differential equations with nonlocal conditions.http://dx.doi.org/10.1155/2013/503656 |
| spellingShingle | Hsiang Liu Cheng-Wen Liao Chin-Tzong Pang Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type Abstract and Applied Analysis |
| title | Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type |
| title_full | Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type |
| title_fullStr | Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type |
| title_full_unstemmed | Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type |
| title_short | Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type |
| title_sort | existence of some semilinear nonlocal functional differential equations of neutral type |
| url | http://dx.doi.org/10.1155/2013/503656 |
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