EXISTENCE OF RESOLVENT FOR VOLTERRA INTEGRAL EQUATIONS ON TIME SCALES
By Murat Adıvar, Youssef N. Raffoul. Bulletin of the Australian Mathematical Society, 2010
56 citations recorded by the source corpus.
Abstract We introduce the concept of ‘shift operators’ in order to establish sufficient conditions for the existence of the resolvent for the Volterra integral equation \[ x(t)=f(t)+\int _{t_{0}}^{t}a(t,s)x(s)\Delta s,\quad t_{0}\in \mathbb {T}^{\kappa }, \] on time scales. The paper will serve as the foundation for future research on the qualitative analysis of solutions of Volterra integral equations on time scales, using the notion of the resolvent.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/dad5848c4f665c437754a17c92c4a9c64431db36
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In Applied Mathematics
In Numerical Analysis
Citations in the corpus
- A new periodicity concept for time scales (2010, background): “Next, we give a generalized version of shift operators (see [2]).”