Abstract
It is well known that it is considerably easier to analyse the solutions of linear integral equations in the case of degenerate kernels than in the general case. In the following we will show that the situation is very much the same for linear integrodifferential equations with degenerate kernels.
AMS Subject Classification 45 J 05, 34 A 10, 34 D 05, 65 L 05, 65 R 05.
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Literature
Bellmann, R.: Stability theory of differential equations. New York: Dover, 1969.
Berg, L.: Asymptotische Lösungen für Operatorgleichungen. Zeitschr. Angew. Math. Mech. 45 (1965) 333–352.
Braaksma, B.L.J.: Recessive solutions of linear differential equations with polynomial coefficients. In: Lecture Notes in Mathematics, vol 280, pp. 1–15. Berlin-Heidelberg-New-York: Springer 1972.
Burton, T.A.: Stability theory for Vol terra equations. Notices of the AMS 26 (1979) A-73.
Cochran, J.A.: The analysis of linear integral equations. New York: McGraw-Hill, 1972.
Davis, H.T.: Introduction to nonlinear differential and integral equations. New York: Dover, 1962.
Gantraacber, F.R.: The theory of matrices, vol 1. New York: Chelsea Publ. Co. 1977.
Goursat, M.E.: Determination de la résolvante d’une classe d’équations intégrales. Bull. sci. Math. 57 (1933) 144–150.
Gröbner, W.: Matrizenrechnung Mannheim: Bibliogr. Institut, 1966.
Hämmerlin, G.: Ein Ersatzkernverfahren zur numerischen Behandlung von Integralgleichungen 2. Art Zeitschr. Angew. Math. Mech. 42 (1962) 439–463.
Hagenbroek, R.J., Kaper, H.G. and Collocation methods for integro-differential equations. SIAM J. Num. Anal. 14 (1977) 377–390.
Hille, E.: Lectures on ordinary differential equations. London: Addison-Wesley, 1969.
Jantscher, L.: Ober das asymptotische Verhalten der Lösungen linearer Integralgleichungen. Journal reine u. angew. Math. 211 (1962) 48–53.
Micchelli, C. A. and Pinkus, A.: Best mean approximation to a 2-dimensional kernel by tensor products. Bull. AMS 83 (1977) 400–402.
Pólya, G. and Szegö, G.: Aufgaben und Lehrsätze aus der Analysis, Bd. 1, 4. Aufl. Berlin-Heidelberg-New York: Springer, 1970.
Riesz, F. and Sz.-Nagy, B.: Vorlesungen über Funktionalanalysis. Berlin: Deutscher Verl. d. Wiss., 1956.
Schaum, H.-J.: Problemorientierbare Verfahren zur numerischen Integration nichtlinearer Integrodifferentialgleichungen Volterraschen Typs. Dissertation, Aachen, 1977.
Schempp, W. and Zeller, K.: (Editors): Constructive theory of functions of several variables. Lecture Notes in Math. vol. 571 Berlin-Heidelberg-New-York: Springer, 1977
Stetter, F.: Analysis of discretization methods for ordinary differential equations. Berlin-Heidelberg-New-York: Springer, 1973.
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Pittnauer, F. (1979). On the Solution of Linear Integrodifferential Equations with Degenerate Kernels. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6289-9_17
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DOI: https://doi.org/10.1007/978-3-0348-6289-9_17
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