Summary
Necessary and sufficient conditions for a linear vector differential system, involving integral, boundary, and vector parameter terms, to be symmetric (self-adjoint) are developed and applied to obtain canonical forms for symmetric problems. In addition, the concept of the equivalence of two such linear problems under nonsingular transformations is examined, and a relationship between equivalence of a problem with its adjoint and symmetry is obtained.
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References
R. H. Cole,General boundary conditions for an ordinary differential system, Trans. Amer. Math. Soc.,111 (1964), pp. 521–550.
W. R. Jones,Differential systems with integral boundary conditions, J. Differential Equations,3 (1967), pp. 191–202.
A. M. Krall,Differential-boundary operators, Trans. Amer. Math. Soc.,154 (1971), pp. 429–458.
A. M. Krall,Stieltjes differential-boundary operators, Proc. Amer. Math. Soc.,41 (1973), pp. 80–86.
W. T. Reid,Ordinary Differential Equations, John Wiley and Sons, New York, 1971.
F. Rellich,Perturbation Theory of Eigenvalue Problems, Lecture Notes, New York University, 1953.
F. Riesz -B. Sz-Nagy,Functional Analysis, Frederick Ungar, New York, 1955, translated fromLeçons d’Analyse Fonctionelle, Budapest, 1952.
O. Vejvoda -M. Tvrdý,Existence of solutions to a linear integro-boundary-differential equation with additional conditions, Ann. Mat. pura ed appl., ser. 4,89 (1971), pp. 169–216.
H. J. Zimmerberg,Symmetric integro-differential-boundary problems, Trans. Amer. Math. Soc.,188 (1974), pp. 407–417.
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Entrata in Redazione il 5 dicembre 1973.
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Zimmerberg, H.J. Linear integro-differential-boundary-parameter problems. Annali di Matematica 105, 241–256 (1975). https://doi.org/10.1007/BF02414932
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DOI: https://doi.org/10.1007/BF02414932