Abstract

Sufficient conditions are derived for existence and uniqueness for the continuous solutions of the Volterra operator integral equations of the first kind with jump discontinuous kernels. Method of steps which is the well-known principle in the theory of functional equations is employed in combination with the method of successive approximations. We also address the case when the solution is not unique and prove the existence of parametric families of solutions and construct them as power-logarithmic asymptotic expansions. The proposed theory is demonstrated for the scalar Volterra equations of the 1st kind with jump discontinuous kernels with applications in evolving dynamical systems modeling.

Related Links: http://studia.complexica.net/index.php?option=com_content&view=article&id=209%3Avolterra-equations-of-the-first-kind-with-discontinuous-kernels-in-the-theory-of-evolving-systems-control-pp-135-146&catid=58%3Anumber-3&Itemid=103&lang=fr – Related paper in Studia Informatica Universalis