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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/503656 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |