Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Cesàro limits
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909377497137152 |
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| author | Appleby, John A. D. Lawless, Emmet |
| author_facet | Appleby, John A. D. Lawless, Emmet |
| contents | In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation functions does not necessarily propagate through to the solution which the classical literature seems to suggest. To illustrate this general idea we show the Cesàro mean of the solution can converge even in cases when the Cesàro mean of the perturbation function diverges. Furthermore we provide a characterisation of when such convergence takes place and explicitly identify the limit in terms of the problem data. Additionally we prove how all results can also be applied to perturbed linear functional differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Cesàro limits Appleby, John A. D. Lawless, Emmet Classical Analysis and ODEs Dynamical Systems In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation functions does not necessarily propagate through to the solution which the classical literature seems to suggest. To illustrate this general idea we show the Cesàro mean of the solution can converge even in cases when the Cesàro mean of the perturbation function diverges. Furthermore we provide a characterisation of when such convergence takes place and explicitly identify the limit in terms of the problem data. Additionally we prove how all results can also be applied to perturbed linear functional differential equations. |
| title | Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Cesàro limits |
| topic | Classical Analysis and ODEs Dynamical Systems |
| url | https://arxiv.org/abs/2407.08416 |