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The method of solution of the boundary value problem applied to a certain fourth order differential equation. (English) Zbl 0699.34018

This paper surveys and also gives new results on the existence of the solution to multi-point boundary value problem associated to the second order linear equation, with parameters \[ y''(t)+[q(t,k,m)+r(t)]y(t)=0. \] The author also discusses a fourth order linear differential equation, existence of conjugate points, oscillatory solutions.
Reviewer: D.Tiba

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A30 Linear ordinary differential equations and systems
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

[1] Vlček V.: On a certain boundary value problem for a fourth-order iterated differential equation. Acta UP Olom., F.R.N., Tom 69, 1981 · Zbl 0486.34012
[2] Borůvka O.: Lineare Differentialtransformationen 2.Ordnung. VEB Deutscher Verlag der Wissenschaften, Berlin, 1967 · Zbl 0153.11201
[3] Greguš M., Neuman F., Arscott F. M.: Three-point boundary value problems in differential equations. J. London Math. Soc. (2), 3 (1971), 429-436 · Zbl 0226.34010 · doi:10.1112/jlms/s2-3.3.429
[4] Arcott F. M.: Two-parameter eigenvalue problems in differential equations. Proc. London Math. Soc. (3), 14 (1964), 459-470
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