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

Vlček, Vladimír

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 88, Math. 26, 149-160 (1987).

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

Keywords:

multi-point boundary value problem; second order linear equation; fourth order linear differential equation; existence of conjugate points; oscillatory solutions

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
[4]	Arcott F. M.: Two-parameter eigenvalue problems in differential equations. Proc. London Math. Soc. (3), 14 (1964), 459-470