Disconjugacy and oscillation of third order differential equations with nonnegative coefficients
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- by G. J. Etgen and C. D. Shih PDF
- Proc. Amer. Math. Soc. 38 (1973), 577-582 Request permission
Abstract:
The purpose of this paper is to establish conditions which imply that the third order linear differential equation with nonnegative coefficients defined on an infinite interval will fail to be disconjugate on any infinite subinterval. Assuming that the equation is not disconjugate on any infinite subinterval, conditions are presented which establish that the equation has oscillatory solutions. These results are in partial answer to questions raised by J. H. Barrett. The oscillation criteria obtained here are similar to the oscillation conditions established by A. C. Lazer.References
- John H. Barrett, Third-order differential equations with nonnegative coefficients, J. Math. Anal. Appl. 24 (1968), 212–224. MR 232039, DOI 10.1016/0022-247X(68)90060-7
- John H. Barrett, Oscillation theory of ordinary linear differential equations, Advances in Math. 3 (1969), 415–509. MR 257462, DOI 10.1016/0001-8708(69)90008-5 G. J. Etgen and C. D. Shih, Disconjugacy of third order differential equations with non-negative coefficients, J. Math. Anal. Appl. (to appear).
- Maurice Hanan, Oscillation criteria for third-order linear differential equations, Pacific J. Math. 11 (1961), 919–944. MR 145160
- A. C. Lazer, The behavior of solutions of the differential equation $y''’+p(x)y^{\prime } +q(x)y=0$, Pacific J. Math. 17 (1966), 435–466. MR 193332
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 577-582
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320432-3
- MathSciNet review: 0320432