Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations |
| |
Authors: | Mikhail V Bulatov Pedro M Lima Ewa B Weinmüller |
| |
Institution: | 1. Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Lermontov Str., 134, 664033, Irkutsk, Russia 2. National Research Irkutsk State Technical University, Lermontov Str., 84, 664074, Irkutsk, Russia 3. Centro de Matemática e Aplica??es, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal 4. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria
|
| |
Abstract: | We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus of the main stream literature, they are interesting, not only in their own right, but also because they may arise from the analysis of certain classes of differential-algebraic systems of partial differential equations. In the first part of the paper, we deal with two-dimensional integral-algebraic equations. Next, we analyze Volterra integral equations of the first kind in which the determinant of the kernel matrix k(t, x) vanishes when t = x. Finally, the third part of the work is devoted to the analysis of degenerate integro-differential systems. The aim of the paper is to specify conditions which are sufficient for the existence of a unique continuous solution to the above problems. Theoretical findings are illustrated by a number of examples. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|