Burton, Theodore Allen and Purnaras, Ioannis K.: Positive kernels, fixed points, and integral equations.
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Abstract
There is substantial literature going back to 1965 showing boundedness properties of solutions of the integro-differential equation x 0 (t) = − Z t 0 A(t − s)h(s, x(s))ds when A is a positive kernel and h is a continuous function using Z T 0 h(t, x(t)) Z t 0 A(t − s)h(s, x(s))dsdt ≥ 0. In that study there emerges the pair: Integro-differential equation and Supremum norm. In this paper we study qualitative properties of solutions of integral equations using the same inequality and obtain results on L p solutions. That is, there occurs the pair: Integral equations and L p norm. The paper also offers many examples showing how to use the L p idea effectively.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2018 |
| Number: | 44 |
| ISSN: | 1417-3875 |
| Page Range: | pp. 1-21 |
| DOI: | https://doi.org/10.14232/ejqtde.2018.1.44 |
| Uncontrolled Keywords: | Integrálegyenlet |
| Additional Information: | Bibliogr.: p. 20-21. ; összefoglalás angol nyelven |
| Date Deposited: | 2019. Jun. 03. 06:13 |
| Last Modified: | 2020. Jul. 29. 12:28 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/58141 |
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