×

A general construction of linear differential equations with solutions of prescribed properties. (English) Zbl 1054.34018

Summary: Effective constructions of ordinary linear differential equations of arbitrary order are presented that give equations with solutions of prescribed qualitative properties, like solutions in the classes \(L^p\), converging to zero or bounded solutions, etc. Connections with transformations of equations and distribution of the zeros of solutions are considered as well. Results generalize those obtained for the second-order linear differential equations.

MSC:

34A55 Inverse problems involving ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Kwong, M.K., On boundedness of solutions of second order differential equations in the limit circle case, (), 242-246 · Zbl 0329.34021
[2] Neuman, F., L2-solutions of y″ = q(t)y and a functional equation, Aequationes math., 6, 162-169, (1971) · Zbl 0225.34022
[3] Neuman, F., Geometrical approach to linear differential equations of the nth order, Rend. mat., 5, 579-602, (1972) · Zbl 0257.34029
[4] Neuman, F., On a problem of transformations between limit-circle and limit-point differential equations, (), 187-193 · Zbl 0334.34022
[5] Neuman, F., On two problems about oscillation of linear differential equations of the third order, J. diff. equations, 15, 589-596, (1974) · Zbl 0287.34029
[6] Neuman, F., Limit circle classification and boundedness of solutions, (), 31-34 · Zbl 0411.34040
[7] Neuman, F., Global properties of linear ordinary differential equations, (), (East European Series) · Zbl 0633.34008
[8] Bartůsěk, M.; Došlá, Z.; Graef, J.R., The nonlinear limit-point/limit-circle problem for higher order equations, Archivum math. (Brno), 34, 13-22, (1998) · Zbl 0914.34023
[9] Došlá, Z., On square integrable solutions of third order linear differential equations, (), 68-72 · Zbl 0977.34007
[10] Everitt, W.N., On the limit-point classification of fourth-order differential equations, J. London math. soc., 44, 273-281, (1969) · Zbl 0162.39201
[11] Patula, W.T.; Wong, J.S.W., An Lp-analogue of the Weyl alternative, Math. ann., 197, 9-28, (1972) · Zbl 0223.34054
[12] Swanson, C.A., Comparison and oscillation theory of linear differential equations, (1968), Acad. Press New York · Zbl 0191.09904
[13] Weyl, H., Über gewöhnliche differentialgleichungen mit singularitäten and die zugehörige entwicklungen willkiirlicher funktionen, Math. ann., 68, 220-269, (1910) · JFM 41.0343.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.