An analogue of Lyapunov’s criterion for (𝑚,𝑛-𝑚)-disfocality

Umamaheswaram, S.

doi:10.1090/S0002-9939-1993-1150655-8

An analogue of Lyapunov’s criterion for $(m,n-m)$-disfocality
HTML articles powered by AMS MathViewer

by S. Umamaheswaram PDF

Proc. Amer. Math. Soc. 117 (1993), 665-671 Request permission

Abstract:

An integral criterion for the $(m,n - m)$-disfocality $(1 \leqslant m \leqslant n - 1)$ on $[a,b]$ of a linear nth order differential equation is given. The criterion is analogous to that of Lyapunov (1947) and Nehari (1962).

References

W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR 0460785, DOI 10.1007/BFb0058618
Uri Elias, Comparison theorems for disfocality and disconjugacy of differential equations, SIAM J. Math. Anal. 15 (1984), no. 5, 922–931. MR 755852, DOI 10.1137/0515069
Uri Elias, Necessary conditions and sufficient conditions for disfocality and disconjugacy of a differential equation, Pacific J. Math. 81 (1979), no. 2, 379–397. MR 547606, DOI 10.2140/pjm.1979.81.379
Paul W. Eloe and Johnny Henderson, Integral conditions for right disfocality of a linear differential equation, J. Math. Anal. Appl. 131 (1988), no. 2, 441–450. MR 935280, DOI 10.1016/0022-247X(88)90217-X
Philip Hartman, On disconjugacy criteria, Proc. Amer. Math. Soc. 24 (1970), 374–381. MR 251304, DOI 10.1090/S0002-9939-1970-0251304-8
Philip Hartman, Ordinary differential equations, S. M. Hartman, Baltimore, Md., 1973. Corrected reprint. MR 0344555
Zeev Nehari, On an inequality of Lyapunov, Studies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 256–261. MR 0145149
S. Umamaheswaram and M. Venkata Rama, Green’s functions for $k$-point focal boundary value problems, J. Math. Anal. Appl. 148 (1990), no. 2, 350–359. MR 1052348, DOI 10.1016/0022-247X(90)90005-Z