In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term ...In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.展开更多
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 wi...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.展开更多
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
文摘In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘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.
