Oscillation criteria for secondorder differential systems
Authors:
Shair Ahmad and C. C. Travis
Journal:
Proc. Amer. Math. Soc. 71 (1978), 247252
MSC:
Primary 34C10
MathSciNet review:
0486792
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Abstract: Sufficient conditions for the oscillation of solutions to the differential system 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.
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 [1]
 S. Ahmad, On positivity of solutions and conjugate points of nonselfadjoint systems (to appear) (see Notices Amer. Math. Soc. 23 (1976), A487, Abstract 76TB134). 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), 1623. MR 0430409 (55:3414)
 [3]
 , An Ndimensional extension of the Sturm separation and comparison theory to a class of nonselfadjoint 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), 510. MR 0322263 (48:625)
 [5]
 W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, SpringerVerlag, Berlin and New York, 1971. MR 0460785 (57:778)
 [6]
 G. J. Etgen and J. F. Pawlowski, Oscillation criteria for second order selfadjoint differential systems, Pacific J. Math. 66 (1976), 99110. 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), 167179. MR 0425241 (54:13198)
 [8]
 A. G. Kartsatos, Oscillation of nonlinear systems of matrix differential equations, Proc. Amer. Math. Soc. 30 (1971), 97101. 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), 331351. 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), 270272. MR 0264163 (41:8759)
 [12]
 E. S. Noussair and C. A. Swanson, Oscillation criteria for differential systems, J. Math. Anal. Appl. 36 (1971), 575580. 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 selfadjoint differential equations, J. London Math. Soc. 6 (1973), 373381. MR 0316824 (47:5372)
 [16]
 C. A. Swanson, Oscillation criteria for nonlinear matrix differential inequalities, Proc. Amer. Math. Soc. 24 (1970), 824827. MR 0259248 (41:3890)
 [17]
 E. C. Tomastik, Oscillation of nonlinear matrix differential equations of second order, Proc. Amer. Math. Soc. 19 (1968), 14271431. MR 0232046 (38:372)
 [18]
 , Oscillation of systems of second order differential equations, J. Differential Equations 9 (1971), 436442. MR 0274863 (43:621)
 [19]
 A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115117. MR 0028499 (10:456a)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197804867922
PII:
S 00029939(1978)04867922
Keywords:
Differential systems,
oscillation
Article copyright:
© Copyright 1978 American Mathematical Society
