References
Aczél, J,Lectures on functional equations and their applications Acad Press, New York London, 1966
Azbelev, N V andCaljuk, Z B,K voprosu o raspredelenii nulej rešenij linejnogo differencial nogo uravnenija tret'ego porjadka Mat Sb (N S)51 (1960), 475–486
Barrett, J H,Oscillation theory of ordinary linear differential equations Adv in Math3 (1986), 415–509
Barvinek, E,O rozloženi nulových bodů řešeni linearní diferenciálni rovnice y′ = Q(t)y a jejich derivaci Acta Math Univ Comenian5 (1961), 465–474
Berkovič, L M,O faktorizacii obyknovennych linějnych differencial nych operatorov, preobrazuemych v operatory s postojannymi koefficientami I + II, Izv Vyssh Uchebn Zaved Aviatsion Tekhn4 (1965), 8–16,12 (1967), 3–14
Besse, A L,Manifolds all of whose geodesics are closed Ergebnisse, Math, 93 Springer, Berlin—New York, 1978
Birkhoff, G D,On the solutions of ordinary linear homogeneous differential equations of the third order Ann of Math12 (1910/11), 103–127
Brioschi, F,Sur les équations différentielles linéaires Bull Soc Math France7 (1879), 105–108
Blanton, G andBaker, J A,Iteration groups generated by C n functions Arch Math (Brno)19 (1982), 121–127
Borůvka, O,Lineare Differentialtransformationen 2 Ordnung VEB, Berlin 1967Linear Differential Transformations of the Second Order The English Univ Press, London, 1971
Borůvka, O,Teorija global nych svojstv obyknovennych linejnych differencial'nych uravněnij vtorogo porjadka Differencial'nyje Uravněnija12 (1976), 1347–1383
Borůvka, O,Algebraic methods in the theory of global properties of the oscillatory equations Y″ = Q(t)Y InEquadiff IV Proceedings, Prague 1977, Lecture Notes in Mathematics, 703 Springer, Berlin—New York, 1979, pp 35–45
Borůvka, O,Sur une classe des groupes continus à un paramètre formés des functions réelles d'une variable Ann Polon Math42 (1982), 27–39
Burton, T A andPatula, W T,Limit circle results for second order equations Monatsh Math81 (1976), 185–194
Čadek, M,Form of general pointwise transformations of linear differential equations Czechoslovak Math J35 (110) (1985), 617–624
Čadek, M,Pointwise transformations of linear differential equations (to appear)
Cartan, É,La théorie des groupes finis et la géometrie différentielle traitees par la methode du repere mobile Gauthier—Villars, 1937
Chanturija, T A,On the oscillation of solutions of higher order linear differential equations (in Russian) Reports of Seminar Vekua Inst Appl Math Univ Tbilissi 16 (1982), 1–74
Chrastina, J,On dispersions of the 1st and 2nd kind of differential equation y″ = q(x)y Publ Fac Sci Univ J E Purkyně, Brno, No508 (1969), 353–377
Coppel, W A,Disconjugacy Lecture notes in mathematics,220 Springer, Berlin 1971
Došlý, O,Phase matrix of linear differential systems Časopis Pěst Mat110 (1985), 183–192
Everitt, W N,Integrable-square, analytic solutions of odd-order, formally symmetric, ordinary differential equations Proc London Math Soc25 (1972), 156–182
Everitt, W N,On the transformation theory of ordinary second-order linear symmetric differential expressions Czechoslovak Math J32 (1982), 275–306
Everitt, W N andNeuman, F,A concept of adjointness and symmetry of differential expressions based on the generalised Lagrange identity and Green's formula InOrdinary differential equations and operators Proceedings, Dundee 1982 Lecture Notes in Mathematics, 1032 Springer, Berlin—New York, 1983, pp 161–169
Forsyth, A R,Invariants covariants and quotient-derivatives associated with linear differential equations Philos Trans Roy Soc London Ser A,179 (1899), 377–489
Greguš, M,Linearna differencialna rovnica tretieho rádu, Veda, Bratislava 1981, extended form in EnglishLinear Differential Equations of the Third Order North Holland & Reidel Co, Dordrecht—Boston—Lancaster, 1986
Guggenheimer, H,Distribution of zeros and limit behavior of solutions of differential equations Proc Amer Math Soc61 (1976), 275–279
Gustafson, G B,Higher order separation and comparison theorems with applications to solution space problems Ann Mat Pura Appl (4)95 (1973), 245–254
Halphen, G H,Memoire sur la reduction des equations differentielles lineaires aux formes integrables Memoires presentes par divers savants a l'academie des sciences de l'Institut de France28 (1884), 1–307
Hanan, M,Oscillation criteria for third-order linear differential equations Pacific J Math11 (1961), 919–944
Hartman, P,On differential equations and the function J 2 μ +Y 2 μ Amer J Math83 (1961), 154–188
Hasse, M andMichler, L,Theorie der Kategorien VEB, Berlin 1966
Hustý, Z,Die Iteration homogener linearer Differentialgleichungen Publ Fac Sci Univ J E Purknyě (Brno)449 (1964), 23–56
Hustý, Z,Über die Transformation und Aquivalenz homogener linearer Differentialgleichungen von hoherer als der zweiten Ordnung I + II + III Czechoslovak Math J15 (90) (1965), 479–502,16 (91) (1966), 1 13,16 (91) (1966), 161–185
Kiguradze, I T,Někotoryje singularnyje krajevyje zadači dlja obyknovennych differencial'nych uravnenij Univ Press Tbilisi 1975
Kondratjev, V A,O koleblemosti rešenij linejnych uravněnij trat ego i četvertogo porjadka Trudy Moskov Mat Obshch8 (1959), 259–282
Kuczma, M,Functional equations in a single variable Podstawy Sterowania Warszawa 1968
Kummer, E E,De generali quadam aequatione differentiali tertii ordinis Progr Evang Konigl Stadtgymnasium Liegnitz 1834 (reprinted in J Reine Angew Math100 (1887), 1–10)
Kwong, M K,On boundedness of solutions of second order differential equations in the limit circle case Proc Amer Math Soc52 (1975), 242–246
Laguerre, E,Sur les equations differentielles lineaires du troisieme ordre C R Acad Sci Paris88 (1879), 116–118
Laitoch, M,Lequation associee dans la theorie des transformation des equations differentielles du second ordre Palack Olomucensis Fac Rerum Natur Chem12 (1963), 45–62
Lazer, A C,The behavior of solutions of the differential equation y‴ +p(x)y + q(x)y = 0 Pacific J Math17 (1966), 435–466
Levin, A Ju,O raspredelenii nulej rešenij linejnogo differencial nogo uravnenija Dokl Akad Nauk SSSR156 (1964), 1281–1284
Lie, S andEngel, F,Theorie der Transformationsgruppe Teubner, Leipzig 1930
Lorch, L, Muldoon, M E andSzegö, P,Higher monotonicity properties of certain Sturm-Liouville functions IV Canad J Math24 (1972), 349–368
Mac Lane, S andBirkhoff, G,Algebra Macmillan, New York 1965
Mammana, G,Decomposizione delle espressioni differenziali lineari omogenee in prodotti di fattori simbolici e applicazione rellativa allo studio delle equazioni differenziali lineari Math Z33 (1931), 186–231
Moravčík, J Über die Åquivalenz linearer gewohnlicher Differentialgleichungen n-ter Ordnung (n = 3,4), Mat Časopis19 (1969), 17–42
Neuman, F,Linear differential equations of the second order and their applications, Rend Mat4 (1971), 559–617
Neuman, F,Geometrical approach to linear differential equations of the n-th order, Rend Mat5 (1972), 579–602 (AbstractSome results on geometrical approach to linear differential equations of the n-th order Comment Math Univ Carolin12 (1971), 307–315)
Neuman, F,Distribution of zeros of solutions of y″ = q(t)y in relation to their behaviour in large Studia Sci Math Hungar8 (1973), 177–185
Neuman, F,On two problems about oscillation of linear differential equations of the third order J Differential Equations15 (1974), 589–596
Neuman, F,On solutions of the vector functional equation y(ξ(x)) = f(x) Ay(x), Aequationes Math16 (1977), 245–257
Neuman, F,Limit circle classification and boundedness of solutions, Proc Roy Soc Edinburgh,81 A (1978), 31–34, also as preprint Zakladni knihovna ČSAV, Praha, No 15688 (April (1977)
Neuman, F,Invarianty linejnych differencial'nych uravněnij 3-go porjadka i metod podvižnogo repera E Kartana Differencial'nyje Uravněnija14 (1979), 398–404
Neuman, F,Second order linear differential systems, Ann Sci, École Norm Sup13 (1980), 437–449
Neuman, F,Factorizations of matrices and functions of two variables Czechoslovak Math J32 (107), 1982, 582–588
Neuman, F,Simultaneous solutions of a system of Abel equations and differential equations with several deviations Czechoslovak Math J32 (107), 1982, 488–494
Neuman, F,A survey of global properties of linear differential equations of the n-th order InOrdinary and Partial Differential Equations Proceedings, Dundee 1982 Lecture Notes in Mathematics, 964, Springer, Boston—New York, 1982, pp 548–563
Neuman, F,Criterion of global equivalence of linear differential equations Proc Roy Soc Edinburgh Sect A97 (1984), 217–221
Neuman, F,Stationary groups of linear differential equations Czechoslovak Math J34 (109) (1984), 645–663 (C R Acad Sci Paris Ser I Math299 (1984), 319–322)
Neuman, F,A note on smoothness of the Stackel transformation Prace Mat WSP Krakow11 (1985), 147–151
Neuman, F,Covariant constructions in the theory of linear differential equations Časopis Pěst Mat111 (1986), 201–207
Neuman, F,Another proof of Borůvka's criterion on global equivalence of the second order linear differential equations (to appear)
Neuman, F,Non-smoothability as an invariant property of coefficients of linear differential equations (to appear)
Posluszny, J andRubel, L A,The motion of an ordinary differential equation J Differential Equations34 (1979), 291–302
Ráb, M,Asymptotische Formeln für die Losungen der Differentialgleichung y″ + q(x)y = 0, Math J14 (89) (1964), 203–221
Sansone, G,Studi sulle equazioni differenziali lineari omogenee di terzo ordine nel campo reale Revista Mat Fis Teor Tucuman6 (1948), 195–253
Schlesinger, L,Handbuch der Theorie der linearen Differentialgleichungen Leipzig, 1897
Šeda, V,Über die Transformation der linearen Differentialgleichungen n-ter Ordnung I + II Časopis Pěst Mat90 (1965), 385–412,92 (1967), 418–435
Stackel, P,Über Transformationen von Differentialgleichungen J Reine Angew Math111 (1893), 290–302
Staněk, S,On an algebraic structure of a group of phases Math Slovaca27 (1977), 423–430
Suchomel, J,Preobrazovanije linejnych odnorodnych differencial'nych uravnenij vysšego porjadka Arch Math (Brno)13 (1977), 41–43
Švec, M,Einige asymptotische und oszillatorische Eigenschaften der Differentialgleichung y‴ + A(x)y′ + B(x)y = 0, Czechoslovak Math J15 (1965) 90, 378–393
Swanson, C A,Comparison and oscillation theory of linear differential equations Acad Press, New York London, 1968
Tryhuk, V,The most general transformation of homogeneous retarded linear differential equations of the n-th order Math Slovaka33 (1983), 15–21
Vosmanský, J,Distribution of zeros of solutions of linear second order differential equations J Differential Equations15 (1979), 1511–1519
Wilczynski, E J,Projective differential geometry of curves and ruled surfaces Teubner, Leipzig, 1906
Zlamal, M,Über asymptotische Eigenschaften der Losengen der linearen Differentialgleichung zweiter Ordnung Czechoslovak Math J6 (81) (1956), 75–93
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Neuman, F. Global theory of ordinary linear homogeneous differential equations in the real domain—I. Aeq. Math. 33, 123–149 (1987). https://doi.org/10.1007/BF01840493
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DOI: https://doi.org/10.1007/BF01840493