The Oscillation of Fourth Order Linear Differential Operators

Lewis, Roger T.

Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 138-145

Résumé

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].

Détail

DOI : 10.4153/CJM-1975-017-4

Bibliographie

[1] 1. Barrett, J. H., Oscillation theory of ordinary linear differential equations, Advances in Math. 3 (1969), 415–509. Google Scholar

[2] 2. Glazman, I. M., Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translation, Jerusalem, 1965. Google Scholar

[3] 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] 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] 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] 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] 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] 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