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Boundary value problems for second order nonhomogeneous differential systems

Author: S. C. Tefteller
Journal: Proc. Amer. Math. Soc. 52 (1975), 271-278
MSC: Primary 34B05
MathSciNet review: 0402156
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Abstract: This paper is a study of second order nonhomogeneous differential systems involving a parameter with boundary conditions specified at two points. By means of a polar coordinate transformation for this system, the existence of eigenvalues is established. The results of this study extend those of Max Mason in that selfadjointness of the problem is not necessary to insure a solution.

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  • [1] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 16, 1022. MR 0069338 (16:1022b)
  • [2] G. J. Etgen and S. C. Tefteller, A two-point boundary problem for nonlinear second order differential systems, SIAM J. Math. Anal. 2 (1971), 64-71. MR 44 #5544. MR 0288346 (44:5544)
  • [3] -, Second order differential equations with general boundary conditions, SIAM J. Math. Anal. 3 (1972), 512-519. MR 47 #538. MR 0311976 (47:538)
  • [4] Max Mason, On the boundary value problems of linear ordinary differential equations of second order, Trans. Amer. Math. Soc. 7 (1906), 337-360. MR 1500753
  • [5] S. C. Tefteller, Oscillation of second order nonhomogeneous linear differential equations, SIAM J. Appl. Math. (to appear). MR 0450681 (56:8974)
  • [6] -, A polar coordinate transformation for nonhomogeneous differential systems (submitted).
  • [7] W. M. Whyburn, Existence and oscillation theorems for non-linear systems of the second order, Trans. Amer. Math. Soc. 30 (1928), 848-854. MR 1501463
  • [8] -, A nonlinear boundary value problem for second order differential systems, Pacific J. Math. 5 (1955), 147-160. MR 16, 1027. MR 0069368 (16:1027d)
  • [9] -, A note on a non-self-adjoint differential system of the second order, J. Elisha Mitchell Sci. Soc. 69 (1953), 116-118.

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Keywords: Nonhomogeneous differential system, polar coordinate transformation, boundary value problem, eigenvalue
Article copyright: © Copyright 1975 American Mathematical Society

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