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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:
34A55Inverse problems of ODE
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References:
[1] Kwong, M. K.: On boundedness of solutions of second order differential equations in the limit circle case. Proc. amer. Math. soc. 52, 242-246 (1975) · 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. Proc. roy. Soc. Edinburgh 72 A, 187-193 (1973/74)
[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. Proc. roy. Soc. Edinburgh 81 A, 31-34 (1978) · Zbl 0411.34040
[7] Neuman, F.: Global properties of linear ordinary differential equations. Mathematics and its applications 52 (1991) · Zbl 0784.34009
[8] Bartusěk, M.; Došlá, Z.; Graef, J. R.: The nonlinear limit-point/limit-circle problem for higher order equations. Archivum math. (Brno) 34, 13-22 (1998)
[9] Došlá, Z.: On square integrable solutions of third order linear differential equations. Proc. ISCM herl’any, 68-72 (1999)
[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) · Zbl 0191.09904
[13] Weyl, H.: Über gewöhnliche differentialgleichungen mit singularitäten and die zugehörige entwicklungen willkiirlicher funktionen. Math. ann. 68, 220-269 (1910) · Zbl 41.0343.01