Oscillatory behavior of third order differential equations

Jones, Gary D.

doi:10.1090/S0002-9939-1974-0333341-1

Oscillatory behavior of third order differential equations
HTML articles powered by AMS MathViewer

by Gary D. Jones PDF

Proc. Amer. Math. Soc. 43 (1974), 133-136 Request permission

Abstract:

It is shown that if $p(x) \leqq 0,q(x) > 0$ and if $y''’ + py’ + qy = 0$ has an oscillatory solution then every nonoscillatory solution is a constant multiple of one nonoscillatory solution.

References

Shair Ahmad and A. C. Lazer, On the oscillatory behavior of a class of linear third order differential equations, J. Math. Anal. Appl. 28 (1969), 681–689. MR 248394, DOI 10.1016/0022-247X(69)90021-3
Michal Greguš, Über einige Eigenschaften der Lösungen der Differentialgleichung $y''’+2Ay’+(A’+b)y=0,$ $A\leq 0$, Czechoslovak Math. J. 11(86) (1961), 106–114 (German, with Russian summary). MR 131028
Maurice Hanan, Oscillation criteria for third-order linear differential equations, Pacific J. Math. 11 (1961), 919–944. MR 145160
Gary D. Jones, An asymptotic property of solutions of $y''’+py^{\prime } +qy=0$, Pacific J. Math. 47 (1973), 135–138. MR 326065
Gary D. Jones, Oscillation properties of third order differential equations, Rocky Mountain J. Math. 3 (1973), 507–513. MR 355193, DOI 10.1216/RMJ-1973-3-3-507
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