SYSTEMS-DISCONJUGACY OF A FOURTH-ORDER DIFFERENTIAL EQUATION WITH A MIDDLE TERM

TitleSYSTEMS-DISCONJUGACY OF A FOURTH-ORDER DIFFERENTIAL EQUATION WITH A MIDDLE TERM
Publication TypeJournal Article
Year of Publication2016
AuthorsBEN AMARA, JAMEL
Secondary TitleCommunications in Applied Analysis
Volume20
Issue1
Start Page25
Pagination12
Date Published01/2016
Type of Workscientific: mathematics
ISSN1083-2564
AMS99Z00
Abstract

Systems-conjugate points have been introduced and studied by John Barrett [3] in relation with the self-adjoint fourth order differential equation (r(x)y ′′) ′′ − (q(x)y ′ ) ′ = p(x)y, where r(x) > 0, p(x) > 0 and q ≡ 0. In this paper we extend some of his results to more general cases, when q(x) is free of any sign restrictions.

URLhttp://www.acadsol.eu/en/articles/20/1/3.pdf
DOI10.12732/caa.v20i1.3
Short TitleSYSTEMS-DISCONJUGACY
Alternate JournalCAA
Refereed DesignationRefereed
Full Text

REFERENCES

[1] F. V. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York
London 1964.
[2] D.Banks and G.Kurowski, A Pr¨ufer transformation for the equation of a vibrating beam,
Trans. Amer. Math. Soc. 199 (1974), 203–222.
[3] J. H. Barrett, Systems-disconjugacy of a fourth order differential equation, Proc. Amer. Math.
Soc. 12 (1961), 205–213.
[4] J. H. Barrett, Oscillation theory of ordinary linear differential equations , Advan. Math. 3
(1969), 415–509.
[5] J. H. Barrett, Two point boundary Problems for self-adjoint linear differential equations of
the fourth order with middle term, Duke Math. J. 29 (1962), 543–554.
[6] Sui-Sun Cheng, Systems-conjugate and focal points of fourth order non-selfadjoint differential
equations, Trans. Amer. Math. Soc. 223 (1976), 155–165.
[7] W. J. Coles, A general Wirtinger-type inequality, Duke Math. J. 27 (1960), 133–138.
[8] L. Greenberg, An oscillation method for fourth-order self-adjoint two point boundary value
Problems with non linear eigenvalues, SIAM J. Math. Anal. 22 (1991), 1021–1042.
[9] W. Leighton, On self-adjoint differential equations of second-order, J. London Math. Society,
35 (1952), 37–47.
[10] W. Leighton, Z. Nehari, On the oscillation of solutions of self-adjoint linear differential equations
of fourth-order, Trans. Amer. Math. Soc. 98 (1958), 325–377.
[11] M. Morse, A generalization of the Sturm separation and comparison theorems in n-space,
Math. Annal. 108 (1930), 53–69.
[12] M. Pfeiffer, Oscillation criteria for self-adjoint fourth-order differential equation, J. Differential
Equations, 46, 1982, p. 194–215.
[13] H. F. Weinberger, Variational Methods for Eigenvalue Approximation, SIAM Philadelphia,
1974.
[14] A. Winter, A criterion of oscillatory stability, Quart. J. Math., V 7, (1949), 115-117.