Abstract
Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.
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Foundation item: Supported by the National Natural Science Foundation of China (10471107) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
Biography: ZHONG Shouguo (1941–), male, Professor, research direction: singular integral equations and their applications.
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Zhong, S. Characteristic singular integral equations with solutions having singularities of higher order on the real axis. Wuhan Univ. J. Nat. Sci. 14, 299–303 (2009). https://doi.org/10.1007/s11859-009-0404-5
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DOI: https://doi.org/10.1007/s11859-009-0404-5
Key words
- characteristic singular integral equation
- Riemann boundary value problem (RBVP)
- solution with singularities of higher order
- real axis