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[E] U. Elias: Oscillation Theory of Two-Term Linear Differential Equations. Kluwer Academic Publishers, Dordrecht, 1996.
[M1] Functional Equations. SNTL, Praha, 1986, pp. 104. (Czech) Zbl 0922.34047
[M2] Global Properties of Linear Ordinary Differential Equations. Mathematics and Its Applications, East European Series 52, Kluwer Academic Publishers (with Academia Praha), Dordrecht, 1991, pp. 334. MR 1192133 | Zbl 0784.34009
[1] Sur les équations différentielles linéaires du second ordre dont les solutions ont des racines formant une suite convexe. Acta Math. Acad. Sci. Hungar. 13 (1962), 281–287. DOI 10.1007/BF02020794 | MR 0148999 | Zbl 0117.30303
[2] On a certain ordering of the vertices of a tree. Časopis Pěst. Mat. 89 (1964), 323–339. MR 0181587 | Zbl 0131.20901
[3] Sur les équations différentielles linéaires oscillatoires du deuxième ordre avec la dispersion fondamentale $\phi (t) = t + \pi $. Bull. Polyt. Inst. Jassy 10 (14) (1964), 37–42. MR 0197825
[4] (with M. Sekanina) Equivalent systems of sets and homeomorphic topologies. Czechoslovak Math. J. 15 (1965), 323–328. MR 0179087
[5] Construction of second-order linear differential equations with solutions of prescribed properties. Arch. Math. (Brno) 1 (1965), 229–246. MR 0199468 | Zbl 0199.13802
[6] On ordering vertices of infinite trees. Časopis Pěst. Mat. 91 (1966), 170–177. MR 0200198 | Zbl 0136.44801
[7] Note on the second phase of the differential equation $ y^{\prime \prime } = q(t)y$. Arch. Math. (Brno) 2 (1966), 56–62. MR 0203127 | Zbl 0217.40201
[8] Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient. Ann. Mat. Pura Appl. 75 (1967), 385–396. DOI 10.1007/BF02416811 | MR 0213652 | Zbl 0148.07104
[9] Extremal property of the equation $y^{\prime \prime } = k^2 y$. Arch. Math. (Brno) 3 (1967), 161–164. MR 0236465 | Zbl 0217.40202
[10] Relation between the distribution of the zeros of the solutions of a 2nd order linear differential equation and the boundedness of these solutions. Acta Math. Acad. Sci. Hungar. 19 (1968), 1–6. DOI 10.1007/BF01894675 | MR 0228750 | Zbl 0162.12304
[11] Centroaffine invariants of plane curves in connection with the theory of the secondorder linear differential equations. Arch. Math. (Brno) 4 (1968), 201–216. MR 0267512
[12] Note on a bounded non-periodic solutions of the second-order linear differential equations with periodic coefficients. Math. Nachrichten 39 (1969), 217–222. DOI 10.1002/mana.19690390403 | MR 0247193
[13] On bounded solutions of a certain differential equation. Proceedings of the Conference on Differential Equations and Their Applications Equadiff 2 Bratislava 1966. Acta Fac. Rerum Natur. Univ. Comenian. Math. 17 (1969), 213–215.
[14] On the coexistence of periodic solutions. J. Differential Equations 8 (1970), 277–282. DOI 10.1016/0022-0396(70)90007-0 | MR 0264168 | Zbl 0208.10903
[15] An explicit form of the differential equation $y^{\prime \prime } = q(t)y$ with periodic solutions. Ann. Mat. Pura Appl. 85 (1970), 295–300. DOI 10.1007/BF02413540 | MR 0262610
[16] On the Liouville transformation. Rend. Mat. 3 (1970), 133–140. MR 0273090 | Zbl 0241.34005
[17] A note on differential equations with periodic solutions. Arch. Math. (Brno) 6 (1970), 189–192. MR 0320411 | Zbl 0241.34028
[18] Construction of differential equations with coexisting periodic solutions. Bull. Polyt. Inst. Jassy 14 (20) (1970), 67–75. MR 0283305 | Zbl 0267.34039
[19] Note on Kummer’s transformation. Arch. Math. (Brno) 6 (1970), 185–188. MR 0294748
[20] Closed plane curves and differential equations. Rend. Mat. 3 (1970), 423–433. MR 0275284 | Zbl 0235.53003
[21] Periodic curvatures and closed curves. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 494–498. MR 0298572 | Zbl 0201.23703
[22] Some results concerning Abel’s equation in the theory of differential equations and consequences for the affine geometry of closed plane curves. Aequationes Math. 4 (1970), 282–284. DOI 10.1007/BF01817786 | MR 1553787
[23] (with F. M. Arscott and M. Greguš) Three-point boundary value problems in differential equations. J. London Math. Soc. (2) 3 (1971), 429–436. MR 0283282
[24] A role of Abel’s equation in the stability theory of differential equations. Aequationes Math. 6 (1971), 66–70. DOI 10.1007/BF01833239 | MR 0299899 | Zbl 0215.43803
[25] $L^2$-solutions of $y^{\prime \prime } = q(t)y$ and a functional equation. Aequationes Math. 6 (1971), 162–169. DOI 10.1007/BF01819748 | MR 0291562 | Zbl 0389.41013
[26] Linear differential equations of the second order and their applications. Rend. Mat. 4 (1971), 559–617. MR 0311972 | Zbl 0227.34005
[27] Some results on geometrical approach to linear differential equations of the $n$-th order. Comment. Math. Univ. Carolin. 12 (1971), 307–315. MR 0288337 | Zbl 0217.12001
[28] A note on Santaló’s isoperimetric theorem. Revista Mat. Fis. Teor. Tucuman 21 (1971), 203–206. MR 0339033 | Zbl 0278.52004
[29] Geometrical approach to linear differential equations of the $n$-th order. Rend. Mat. 5 (1972), 579–602. MR 0324141 | Zbl 0257.34029
[30] Oscillation in linear differential equations. Proceedings of the Conference Equadiff 3, J. E. Purkyně University, Brno, 1972, pp. 119–125. MR 0350114
[31] Distribution of zeros of solutions of $y^{\prime \prime }=q(t) y$ in relation to their behaviour in large. Studia Sci. Math. Hungar. 8 (1973), 177–185. MR 0333344 | Zbl 0286.34050
[32] On $n$-dimensional closed curves and periodic solutions of linear differential equations of the $n$-th order. Demonstratio Mat. 6 (1973), 329–337. MR 0364757 | Zbl 0286.34063
[33] On a problem of transformations between limit-circle and limit-point differential equations. Proc. Roy. Soc. Edinburgh Sect. A 72 (1973/74), 187–193. MR 0385226
[34] On two problems about oscillation of linear differential equations of the third order. J. Differential Equations 15 (1974), 589–596. DOI 10.1016/0022-0396(74)90075-8 | MR 0342769
[35] Global transformation of linear differential equations of the $n$-th order. Knižnice odb. a věd. spisů VUT Brno B-56 (1975), 165–171.
[36] On solutions of the vector functional equation $y(\xi (x))=f(x)\cdot A \cdot y(x)$. Aequationes Math. 16 (1977), 245–257. DOI 10.1007/BF01836037 | MR 0467061 | Zbl 0375.34013
[37] (with J. Vosmanský) On functions (sequences) the derivatives (differences) of which are of constant sign. Doklady Ak. Nauk Azer. SSR 34 (1978), 8–12. (Russian)
[38] (with S. Staněk) On the structure of second-order periodic differential equations with given characteristic multipliers. Arch. Math. (Brno) 13 (1977), 149–157. MR 0460790
[39] Linear differential equations with periodic coefficients in the critical case. An. Sti. Univ. Al. I. Cuza Jassy Sect. I a Mat. 23 (1977), 325–328. MR 0486816 | Zbl 0373.34020
[40] Categorial approach to global transformations of the $n$-th order linear differential equations. Časopis Pěst. Mat. 1977 102, 350–355. MR 0477284 | Zbl 0374.34028
[41] Limit circle classification and boundnedness of solutions. Proc. Roy. Soc. Edinburgh 81 A (1978), 31–34. MR 0529374
[42] Global properties of the $n$-th order linear differential equations. Proceedings of Equadiff  4 Praha 1977, Lecture Notes in Mathematics 703, Springer, Berlin, 1979, pp. 309–319. MR 0535351
[43] Invariants of third order linear differential equations and Cartan’s moving frame method. Differencial’nyje Uravnenija 14 (1979), 398–404. (Russian)
[44] A generalization of Floquet theory. Acta Math. Univ. Comenian. 39 (1980), 53–59. MR 0619262 | Zbl 0517.34035
[45] Transformations of linear differential equations of the $n$-th order. Sborník 6. vědecké konference Vysoké školy dopravní v Žilině Sept. 1979, VŠD Žilina, 1979, pp. 11–19. (Russian)
[46] On transformations of differential equations and systems with deviating argument. Czechoslovak Math. J. 31 (1981), 87–90. MR 0604115 | Zbl 0463.34051
[47] Global theory of linear differential equations of the $n$-th order. Proceedings of the Colloquium on Qualitative Theory of Differential Equations Szeged-Hungary August 1979, Ser. Coll. Math. Soc. J. Bolyai, North-Holland Publ. Co., 1981, pp. 777–793. MR 0680619 | Zbl 0484.34022
[48] Second order linear differential systems. Ann. Sci. École Norm. Super. (Paris) 13 (1980), 437–449. MR 0608288 | Zbl 0453.34006
[49] Functions of two variables and matrices involving factorizations. C. R. Math. Rep. Acad. Sci. Canada 3 (1981), 7–11. MR 0608675 | Zbl 0449.15009
[50] Factorizations of matrices and functions of two variables. Czechoslovak Math. J. 32 (1982), 582–588. MR 0682133 | Zbl 0517.15012
[51] Functions of the form $_{i=1}^N f_i (x)g_i(t)$ in $L_2$. Arch. Math. (Brno) 18 (1982), 19–22.
[52] Simultaneous solutions of a system of Abel equations and differential equations with several deviations. Czechoslovak Math. J. 32 (1982), 488–494. MR 0669790 | Zbl 0524.34070
[53] Global canonical forms of linear differential equations. Math. Slovaca 33 (1983), 389–394. MR 0720509 | Zbl 0527.34036
[54] Linear differential equations—global theory. Proceedings of Equadiff 5 Bratislava 1981, Teubner-Texte zur Mathematik, Leipzig, 1982, pp. 272–275. MR 0715934 | Zbl 0519.34004
[55] Theory of global properties of ordinary differential equations of the $n$-th order. Differencial’nyje Uravnenija 19 (1983), 799–808. (Russian) MR 0703421
[56] A survey of global properties of linear differential equations of the $n$-th order. Proceedings of the Conference on Ordinary and Partial Differential Equations, Dundee 1982, Lecture Notes in Mathematics 964, Springer, Berlin, pp. 548–563. MR 0693139 | Zbl 0501.34003
[57] (with W. N. Everitt) A concept of adjointness and symmetry of differential expressions based on the generalized Lagrange identity and Green’s formula. Proceedings: Ordinary Differential Equations and Operators, Dundee 1982, Lecture Notes in Mathematics 1032, Springer, Berlin, pp. 161–169. MR 0742639
[58] From local to global investigations of linear differential equations of the $n$-th order. Jahrbuch Überblicke Mathematik 1984, 55–80. Zbl 0548.34009
[59] Criterion of global equivalence of linear differential equations. Proc. Roy. Soc. Edinburgh 97 A (1984), 217–221. MR 0751194 | Zbl 0552.34009
[60] Stationary groups of linear differential equations. Czechoslovak Math. J. 34 (1984), 645–663. MR 0764446 | Zbl 0573.34028
[61] A vector functional equation and linear differential equations. Aequationes Math. 29 (1985), 19–23. MR 0812301 | Zbl 0593.39006
[62] A note on smoothness of the Stäckel transformation. Prace Mat. WSP (Kraków) 11 (1985), 147–151.
[63] Covariant constructions in the theory of linear differential equations. Časopis Pěst. Mat. 111 (1986)), 201–207. MR 0847318 | Zbl 0597.34005
[64] Global theory of ordinary linear homogeneous differential equations in the real domain I, II. Aequationes Math. 33 (1987), 123–149. DOI 10.1007/BF01836159 | MR 0911150
[65] Solution to the Problem No. 10 of N. Kamran. Proceedings of the 23rd Intern. Symp. on Functional Equations Gargnano-Italy 1985, Univ. of Waterloo, Ont. Canada, pp. 60–62.
[66] Ordinary linear differential equations—a survey of the global theory. Proceedings of Equadiff 6 Brno 1986, Lecture Notes in Mathematics 1192, Springer, Berlin, pp. 59–70. MR 0877107 | Zbl 0633.34008
[67] Oscillatory behavior of iterative linear ordinary differential equations depends on their order. Arch. Math. (Brno) 22 (1986), 187–192. MR 0868533 | Zbl 0608.34036
[68] On iteration groups of certain functions. Arch. Math. (Brno) 25 (1989), 185–194. MR 1188063 | Zbl 0721.39002
[69] Another proof of Borůvka’s criterion on global equivalence of the second order ordinary linear differential equations. Časopis Pěst. Mat. 115 (1990), 73–80. MR 1044016 | Zbl 0714.34055
[70] Smoothness as an invariant property of coefficients of linear differential equations. Czechoslovak Math. J. 39 (1989), 513–521. MR 1006317 | Zbl 0702.34034
[71] On a canonical parametrization of continuous functions. Opuscula Math. (Kraków) 1335 (1990)), 185–191. MR 1120254 | Zbl 0779.39002
[72] On Halphen and Laguerre-Forsyth canonical forms of linear differential equations. Arch. Math. (Brno) 26 (1990), 147–154. MR 1188274 | Zbl 0729.34008
[73] Transformations and canonical forms of functional-differential equations. Proc. Roy. Soc. Edinburgh 115 A (1990), 349–357. MR 1069527
[74] Finite sums of products of functions in single variables. Linear Algebra Appl. 134 (1990), 153–164. DOI 10.1016/0024-3795(90)90014-4 | MR 1060018 | Zbl 0714.26007
[75] (with Th. M. Rassias) Functions decomposable into finite sums of products. Constantin Carathéodory—An International Tribute, Vol. II, World Scientific Publ. Co., Singapore, 1991, pp. 956–963.
[76] Ordered groups commuting matrices and iterations of functions in transformations of differential equations. Constantin Carathéodory—An International Tribute, Vol. II, World Scientific Publ. Co., Singapore, 1991, pp. 942–955. MR 1130872 | Zbl 0737.34023
[77] (with Á. Elbert and J. Vosmanský) Principal pairs of solutions of linear second order oscillatory differential equations. Differential Integral Equations 5 (1992), 945–960. MR 1167505
[78] On transformation of quasilinear differential equations to canonical forms. Recent Trends in Ordinary Differential Equations Vol. I, World Scientific Series in Applicable Analysis World Sci., Singapore, 1992, pp. 457–461. MR 1180130 | Zbl 0832.34026
[79] On the $n$-th order iterative linear ordinary differential equations. Aequationes Math. 46 (1993), 38–43. DOI 10.1007/BF01833996 | MR 1220720
[80] (with Á. Elbert) Exceptional solutions of Hill equations. J. Differential Equations 116 (1995), 419–430. DOI 10.1006/jdeq.1995.1041 | MR 1318581
[81] Limit behavior of ordinary linear differential equations. Proceedings of Georgian Academy of Sciences Mathematics 1 (1993), 355–364. MR 1262570
[82] (with M. Muldoon) Principal pairs for oscillatory second order linear differential equations. Dynamical Systems and Applications, World Scientific Series in Applicable Analysis World Sci. Vol. 4, Singapore, 1995, pp. 517–526. MR 1372981
[83] On equivalence of linear functional-differential equations. Results in Mathematics 26 (1994), 354–359. DOI 10.1007/BF03323059 | MR 1300618 | Zbl 0829.34054
[84] Nonextendable classes of linear differential equations. J. Nonlinear Anal. 25 (1995), 1045–1049. DOI 10.1016/0362-546X(95)00098-G | MR 1350726 | Zbl 0843.34012
[85] Solutions of Abel’s equation in relation to asymptotic behaviour of linear differential equations. Aequationes Math, Accepted.
[86] Transformation theory of linear ordinary differential equations—from local to global investigations. Archivum Math. (Brno) 33 (1997), 65–74. MR 1464302 | Zbl 0914.34012
[87] Dispersions for linear differential equations of arbitrary order. Archivum Math. (Brno) 33 (1997), 147–155. MR 1464309 | Zbl 0914.34010
[88] Asymptotic behaviour and zeros of solutions on $n$-th order linear differential equations. 8Submitted.
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