Oscillatory properties of linear third-order differential equations.
Author:
W. J. Kim
Journal:
Proc. Amer. Math. Soc. 26 (1970), 286-293
MSC:
Primary 34.42
DOI:
https://doi.org/10.1090/S0002-9939-1970-0264162-2
MathSciNet review:
0264162
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Separation theorems, distribution of zeros of solutions, and disconjugacy criteria for linear third-order differential equations are discussed. For instance, it is proved that the equation $y''’ + py'' + qy’ + ry = 0$, where $p \in C'',q \in C’$, and $r \in C$ on an interval $I$, is disconjugate on $I$ if $p$ does not change sign and if $q \leqq 0,r \geqq 0,q - 2p’ \leqq 0$, and $r - q’ + p'' \leqq 0$ on $I$.
- N. V. Azbelev and Z. B. Calyuk, On the question of the distribution of the zeros of solutions of a third-order linear differential equation, Mat. Sb. (N.S.) 51 (93) (1960), 475–486 (Russian). MR 0121529
- John H. Barrett, Third-order differential equations with nonnegative coefficients, J. Math. Anal. Appl. 24 (1968), 212–224. MR 232039, DOI https://doi.org/10.1016/0022-247X%2868%2990060-7
- John H. Barrett, Oscillation theory of ordinary linear differential equations, Advances in Math. 3 (1969), 415–509. MR 257462, DOI https://doi.org/10.1016/0001-8708%2869%2990008-5
- Maurice Hanan, Oscillation criteria for third-order linear differential equations, Pacific J. Math. 11 (1961), 919–944. MR 145160
- W. J. Kim, Disconjugacy and disfocality of differential systems, J. Math. Anal. Appl. 26 (1969), 9–19. MR 236464, DOI https://doi.org/10.1016/0022-247X%2869%2990172-3
- 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
- J. Mikusiński, Sur l’équation $x^{(n)}+A(t)x=0$, Ann. Polon. Math. 1 (1955), 207–221 (French). MR 86201, DOI https://doi.org/10.4064/ap-1-2-207-221
- G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), no. 4, 312–324. MR 1501228, DOI https://doi.org/10.1090/S0002-9947-1922-1501228-5
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.42
Retrieve articles in all journals with MSC: 34.42
Additional Information
Keywords:
Zeros of solutions,
separation,
distribution of zeros,
sufficient conditions for disconjugacy,
linear equations,
ordinary,
third-order,
real-valued coefficients
Article copyright:
© Copyright 1970
American Mathematical Society