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The Oscillation of Fourth Order Linear Differential Operators

Published online by Cambridge University Press:  20 November 2018

Roger T. Lewis
Roger T. Lewis*
Affiliation:
Slippery Rock State College, Slippery Rock, Pennsylvania
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Define the self-adjoint operator

where r(x) > 0 on (0, ∞) and q and p are real-valued. The coefficient q is assumed to be differentiate on (0, ∞) and r is assumed to be twice differentia t e on (0, ∞).

The oscillatory behavior of L4 as well as the general even order operator has been considered by Leigh ton and Nehari [5], Glazman [2], Reid [7], Hinton [3], Barrett [1], Hunt and Namb∞diri [4], Schneider [8], and Lewis [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 138 - 145
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Barrett, J. H., Oscillation theory of ordinary linear differential equations, Advances in Math. 3 (1969), 415–509.Google Scholar
2. Glazman, I. M., Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translation, Jerusalem, 1965.Google Scholar
3. Hinton, D. B., Clamped end boundary conditions for fourth-order self-adjoint differential equations, Duke Math. J. 34 (1967), 131–138.Google Scholar
4. Hunt, R. W. and Namb∞diri, M. S. T., Solution behaviour for general self-adjoint differential equations, Proc. London Math. Soc. 21 (1970), 637–50.Google Scholar
5. Leighton, W. and Nehari, Z., On the oscillation of solutions of self-adjoint differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325–77.Google Scholar
6. Lewis, R. T., Oscillation and nonosdilation criteria for some self-adjoint even order linear differential operators, Pacific J. Math. 51 (1974), 221–234.Google Scholar
7. Reid, W. T., Riccati matrix differential equations and nonoscillation criteria for associated linear systems, Pacific J. Math. 13 (1963), 665–85.Google Scholar
8. Schneider, L. J., Oscillation properties of the 2–2 disconjugate fourth self-adjoint differential equation, Proc. Amer. Math. Soc. 28 (1971), 545–550.Google Scholar