Positive kernels, fixed points, and integral equations
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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2018
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Integrálegyenlet |
| doi: | 10.14232/ejqtde.2018.1.44 |
| Online Access: | http://acta.bibl.u-szeged.hu/58141 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 1-21 |
| ISSN: | 1417-3875 |