Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Oscillation criteria for second-order differential systems


Authors: Shair Ahmad and C. C. Travis
Journal: Proc. Amer. Math. Soc. 71 (1978), 247-252
MSC: Primary 34C10
MathSciNet review: 0486792
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions for the oscillation of solutions to the differential system $ X''(t) + A(t)X(t) = 0$ are established which are valid when the matrix A is not symmetric. An example is given to demonstrate that a condition known to be sufficient for the oscillation of solutions when A is symmetric is not valid in the nonsymmetric case.


References [Enhancements On Off] (What's this?)

  • [1] S. Ahmad, On positivity of solutions and conjugate points of nonselfadjoint systems (to appear) (see Notices Amer. Math. Soc. 23 (1976), A-487, Abstract 76T-B134). MR 539335 (80h:34038)
  • [2] S. Ahmad and A. C. Lazer, On the components of extremal solutions of second order systems, SIAM J. Math. Anal. 8 (1977), 16-23. MR 0430409 (55:3414)
  • [3] -, An N-dimensional extension of the Sturm separation and comparison theory to a class of nonself-adjoint systems, SIAM J. Math. Anal. (to appear). MR 512517 (80a:34035)
  • [4] W. Allegretto and L. Erbe, Oscillation criteria for matrix differential inequalities, Canad. Math. Bull. 16 (1973), 5-10. MR 0322263 (48:625)
  • [5] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin and New York, 1971. MR 0460785 (57:778)
  • [6] G. J. Etgen and J. F. Pawlowski, Oscillation criteria for second order self-adjoint differential systems, Pacific J. Math. 66 (1976), 99-110. MR 0440147 (55:13027)
  • [7] R. D. Gentry and C. C. Travis, Comparison of eigenvalues associated with linear differential equations of arbitrary order, Trans. Amer. Math. Soc. 223 (1976), 167-179. MR 0425241 (54:13198)
  • [8] A. G. Kartsatos, Oscillation of nonlinear systems of matrix differential equations, Proc. Amer. Math. Soc. 30 (1971), 97-101. MR 0280798 (43:6517)
  • [9] M. S. Keener and C. C. Travis, Focal points and positive cones for a class of nth order differential equations, Trans. Amer. Math. Soc. 237 (1978), 331-351. MR 479377 (80i:34050)
  • [10] -, Sturmian theory for a class of nonselfadjoint differential systems (to appear).
  • [11] K. Kreith, Oscillation criteria for nonlinear matrix differential equations, Proc. Amer. Math. Soc. 26 (1970), 270-272. MR 0264163 (41:8759)
  • [12] E. S. Noussair and C. A. Swanson, Oscillation criteria for differential systems, J. Math. Anal. Appl. 36 (1971), 575-580. MR 0296417 (45:5477)
  • [13] W. T. Reid, Ordinary differential equations, Wiley, New York, 1971. MR 0273082 (42:7963)
  • [14] K. Schmitt and H. L. Smith, Positive solutions and conjugate points for systems of differential equations (to appear). MR 512658 (80a:34033)
  • [15] W. Simons, Disconjugacy criteria for systems of self-adjoint differential equations, J. London Math. Soc. 6 (1973), 373-381. MR 0316824 (47:5372)
  • [16] C. A. Swanson, Oscillation criteria for nonlinear matrix differential inequalities, Proc. Amer. Math. Soc. 24 (1970), 824-827. MR 0259248 (41:3890)
  • [17] E. C. Tomastik, Oscillation of nonlinear matrix differential equations of second order, Proc. Amer. Math. Soc. 19 (1968), 1427-1431. MR 0232046 (38:372)
  • [18] -, Oscillation of systems of second order differential equations, J. Differential Equations 9 (1971), 436-442. MR 0274863 (43:621)
  • [19] A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115-117. MR 0028499 (10:456a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0486792-2
Keywords: Differential systems, oscillation
Article copyright: © Copyright 1978 American Mathematical Society