We consider the multidimensional abstract linear integral equation of Volterra type (1), as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functi...We consider the multidimensional abstract linear integral equation of Volterra type (1), as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Banach space-valued defined on a compact interval R of , R <SUB>t </SUB>is a subinterval of R depending on t ∈ R and (⋆) ∫ denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems. The Henstock integral setting enables us to consider highly oscillating functions.展开更多
In this work we establish an existence theorem of regulated solutions for a class of Stieltjes equations which involve generalized fuemann kind of integrals. The general method spplied consists in considering the cont...In this work we establish an existence theorem of regulated solutions for a class of Stieltjes equations which involve generalized fuemann kind of integrals. The general method spplied consists in considering the continuous-time Stieltjes equation as limit of discrete processes. This approach will prove fruitful in the study of the controllability of Stieltjes systems, because it will be possible to get properties on the continuous time equation by transferring properties of the discrete ones.展开更多
The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-typewhere the functions are Banach-space valued. Special theorems on existence o...The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-typewhere the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgu3 integral setting are obtained. These sharpen earlier results.展开更多
文摘We consider the multidimensional abstract linear integral equation of Volterra type (1), as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Banach space-valued defined on a compact interval R of , R <SUB>t </SUB>is a subinterval of R depending on t ∈ R and (⋆) ∫ denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems. The Henstock integral setting enables us to consider highly oscillating functions.
基金This work was developed at the Institute of Mathematics of the Czech Republic Academy of Sciences atPraha, with financial supp
文摘In this work we establish an existence theorem of regulated solutions for a class of Stieltjes equations which involve generalized fuemann kind of integrals. The general method spplied consists in considering the continuous-time Stieltjes equation as limit of discrete processes. This approach will prove fruitful in the study of the controllability of Stieltjes systems, because it will be possible to get properties on the continuous time equation by transferring properties of the discrete ones.
文摘The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-typewhere the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgu3 integral setting are obtained. These sharpen earlier results.
