Symmetric integro-differential-boundary problems
HTML articles powered by AMS MathViewer
- by Hyman J. Zimmerberg PDF
- Trans. Amer. Math. Soc. 188 (1974), 407-417 Request permission
Abstract:
Necessary and sufficient conditions for a linear vector integro-differential-boundary problem to be symmetric (selfadjoint) are developed, and then applied to obtain canonical forms of such symmetric problems. Moreover, the formulation of the integro-boundary conditions herein yields a simplification of one of the conditions for selfadjointness of a differential-boundary operator previously announced.References
- Randal H. Cole, General boundary conditions for an ordinary linear differential system, Trans. Amer. Math. Soc. 111 (1964), 521–550. MR 159979, DOI 10.1090/S0002-9947-1964-0159979-0
- William R. Jones, Differential systems with integral boundary conditions, J. Differential Equations 3 (1967), 191–202. MR 206388, DOI 10.1016/0022-0396(67)90024-1
- Allan M. Krall, Differential-boundary operators, Trans. Amer. Math. Soc. 154 (1971), 429–458. MR 271445, DOI 10.1090/S0002-9947-1971-0271445-4
- William T. Reid, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0273082
- O. Vejvoda and M. Tvrdý, Existence of solutions to a linear integro-boundary-differential equation with additional conditions, Ann. Mat. Pura Appl. (4) 89 (1971), 169–216. MR 316988, DOI 10.1007/BF02414947
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 188 (1974), 407-417
- MSC: Primary 45J05
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338717-9
- MathSciNet review: 0338717