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15.—A Class of Focal Points for Non-self-adjoint Fourth-order Differential Equations

Published online by Cambridge University Press:  14 February 2012

Kurt Kreith
Kurt Kreith
Affiliation:
Chelsea College, University of London*
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Synopsis

Conjugate points are defined in terms of solutions of a linear fourth-order differential equation satisfying two homogeneous boundary conditions at x = α and either u(β) = u′(β) = 0 or u′(γ) = u″(γ) = 0. The smallest β > α and γ > α such that these boundary conditions are satisfied by a non-trivial solution of the equation are denoted by η(α) and ῆ-(α), respectively. Upper bounds are established for min [η(α), ῆ(α)] relative to the conjugate points of a self-adjoint differential equation which is majorised by the more general equation under study.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 3 , 1975 , pp. 207 - 214
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References To Literature

[1]Kreith, K., 1971 Disconjugacy criteria for nonselfadjoint differential equations of even order, Can. Jl Math., 23, 644–652.Google Scholar
[2]Kreith, K., 1972 Oscillation properties of nonselfadjoint differential equations of even order. Proc. Conf. Ordinary and Partial Diff. Eqns, Dundee, 294–297.Springer Verlag.Google Scholar
[3]Ince, E. L., 1944 Ordinary Differential Equations. New York:Dover.Google Scholar
[4]Kreith, K., 1970 A comparison theorem for conjugate points of general selfadjoint differential equations. Proc. Amer. Math. Soc., 25, 656–661.Google Scholar
[5]Leighton, W., 1970 Quadratic functions of second order. Trans. Amer. Math. Soc., 151, 309–322.(Issued 23 May 1975)Google Scholar