A Nonstandard Volterra Integral Equation on Time Scales

Demonstratio Mathematica 2019
Andrejs Reinfelds, Shraddha Ramanbhai Christian

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach's fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

Keywords
Volterra integral equations, time scales, bounded solution, continuous dependence
DOI
10.1515/dema-2019-0042
Hyperlink
https://www.degruyter.com/document/doi/10.1515/dema-2019-0042/html

Reinfelds, A., Christian, S. A Nonstandard Volterra Integral Equation on Time Scales. Demonstratio Mathematica, 2019, Vol. 52, No. 1, pp.503-510. ISSN 2391-4661. Available from: doi:10.1515/dema-2019-0042

Publication language
English (en)