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Sign Properties of Green's Functions For Two Classes of Boundary Value Problems

  • P. W. Eloe (a1)
Abstract

Let G(x,s) be the Green's function for the boundary value problem y(n) = 0, Ty = 0, where Ty = 0 represents boundary conditions at two points. The signs of G(x,s) and certain of its partial derivatives with respect to x are determined for two classes of boundary value problems. The results are also carried over to analogous classes of boundary value problems for difference equations.

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COPYRIGHT: © Canadian Mathematical Society 01
References
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1. Coddington, E.A and Levinson, N., “Theory of Ordinary Differential Equations,” McGraw-Hill, New York, 1955.
2. Coppel, W.A, “Disconjugacy” Lecture Notes in Mathematics 220, Springer-Verlag, New York/Berlin, 1971.10.1007/BFb0058618
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8. Peterson, A.C, Boundary value problems for an n-th order linear difference equation, SIAM J. Math. Anal. 15 (1984), pp. 124–132.
9. Ridenhour, J., On the sign of Green s functions for multipoint boundary value problems, Pacific J. Math., 92(1981), pp. 141–150.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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