Oscillation properties of two term linear differential equations
HTML articles powered by AMS MathViewer
- by G. A. Bogar PDF
- Trans. Amer. Math. Soc. 161 (1971), 25-33 Request permission
Abstract:
The two term differential equations ${L_n}[y] + py = 0$, where ${L_0}[y] = y,{L_i}[y] = ({\rho _i}(t){L_i}[y(t)])’$, were recently studied by Z. Nehari. In this paper we give integral conditions which assure the integrability of $\rho _1^{ - 1}(t)p(t)$ on $[a,\infty )$ when ${L_n}[y]$ is disconjugate. By changing the integral conditions slightly we then prove that the equation has n linearly independent oscillatory solutions.References
- Robert W. Hunt, Oscillation properties of even-order linear differential equations, Trans. Amer. Math. Soc. 115 (1965), 54–61. MR 203132, DOI 10.1090/S0002-9947-1965-0203132-X
- Walter Leighton and Zeev Nehari, On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325–377. MR 102639, DOI 10.1090/S0002-9947-1958-0102639-X R. A. Leslie, The zeros of solutions to certain linear homogeneous differential equations of even order, Doctoral Dissertation, University of Georgia, Athens, Ga., 1968.
- J. Mikusiński, Sur l’équation $x^{(n)}+A(t)x=0$, Ann. Polon. Math. 1 (1955), 207–221 (French). MR 86201, DOI 10.4064/ap-1-2-207-221
- Zeev Nehari, Non-oscillation criteria for $n-th$ order linear differential equations, Duke Math. J. 32 (1965), 607–615. MR 186883
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 161 (1971), 25-33
- MSC: Primary 34.42
- DOI: https://doi.org/10.1090/S0002-9947-1971-0284646-6
- MathSciNet review: 0284646