Boundary value problems for second order nonhomogeneous differential systems
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- by S. C. Tefteller PDF
- Proc. Amer. Math. Soc. 52 (1975), 271-278 Request permission
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.References
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- 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 288346, DOI 10.1137/0502007
- G. J. Etgen and S. C. Tefteller, Second order differential equations with general boundary conditions, SIAM J. Math. Anal. 3 (1972), 512–519. MR 311976, DOI 10.1137/0503049
- Max Mason, On the boundary value problems of linear ordinary differential equations of second order, Trans. Amer. Math. Soc. 7 (1906), no. 3, 337–360. MR 1500753, DOI 10.1090/S0002-9947-1906-1500753-1
- S. C. Tefteller, Oscillation of second order nonhomogeneous linear differential equations, SIAM J. Appl. Math. 31 (1976), no. 3, 461–467. MR 450681, DOI 10.1137/0131039 —, A polar coordinate transformation for nonhomogeneous differential systems (submitted).
- William M. Whyburn, Existence and oscillation theorems for non-linear differential systems of the second order, Trans. Amer. Math. Soc. 30 (1928), no. 4, 848–854. MR 1501463, DOI 10.1090/S0002-9947-1928-1501463-1
- William M. Whyburn, A nonlinear boundary value problem for second order differential systems, Pacific J. Math. 5 (1955), 147–160. MR 69368 —, A note on a non-self-adjoint differential system of the second order, J. Elisha Mitchell Sci. Soc. 69 (1953), 116-118.
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 271-278
- MSC: Primary 34B05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0402156-9
- MathSciNet review: 0402156