Oscillating solutions of third order differential equations
HTML articles powered by AMS MathViewer
- by W. R. Utz
- Proc. Amer. Math. Soc. 26 (1970), 273-276
- DOI: https://doi.org/10.1090/S0002-9939-1970-0262602-6
- PDF | Request permission
Abstract:
Third order ordinary linear differential equations are investigated with respect to the property of having a basis for solutions that consist of three oscillating solutions yet some nontrivial solution of the equation is nonoscillatory.References
- George D. Birkhoff, On the solutions of ordinary linear homogeneous differential equations of the third order, Ann. of Math. (2) 12 (1911), no. 3, 103–127. MR 1503560, DOI 10.2307/2007241
- J. M. Dolan, On the relationship between the oscillatory behavior of a linear third-order differential equation and its adjoint, J. Differential Equations 7 (1970), 367–388. MR 255908, DOI 10.1016/0022-0396(70)90116-6
- 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
- C. M. Petty and J. E. Barry, A geometrical approach to the second-order linear differential equation, Canadian J. Math. 14 (1962), 349–358. MR 146451, DOI 10.4153/CJM-1962-027-x
- Marko Švec, Sur une propriété des intégrales de l’équation $y^{(n)}+Q(x)y=0,$, $n=3,\,4$, Czechoslovak Math. J. 7(82) (1957), 450–462 (French, with Russian summary). MR 95313
- C. A. Swanson, Comparison and oscillation theory of linear differential equations, Mathematics in Science and Engineering, Vol. 48, Academic Press, New York-London, 1968. MR 0463570
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 26 (1970), 273-276
- MSC: Primary 34.42
- DOI: https://doi.org/10.1090/S0002-9939-1970-0262602-6
- MathSciNet review: 0262602