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References (14)
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- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266112100102
- Publisher site
- See Article on Publisher Site
Abstract
We prove a theorem on the reduction of the Goursat problem in integral form to an equivalent system of two Fredholm integral equations of the second kind and a uniqueness theorem for its solution. We suggest a method for reducing nonlocal characteristic and mixed problems, including the Samarskii problem for a second-order differential equation, to local problems for partial differential equations of higher order. We present examples illustrating the importance of the condition ensuring the uniqueness of the solution of the problems in question.
Journal
Differential Equations – Springer Journals
Published: Dec 15, 2012