@article{106988, author = {Ivan Kiguradze}, title = {On the oscillatory and monotone solutions of ordinary differential equations}, journal = {Archivum Mathematicum}, volume = {014}, year = {1978}, pages = {21-44}, zbl = {0408.34033}, mrnumber = {512742}, language = {en}, url = {http://dml.mathdoc.fr/item/106988} }
Kiguradze, Ivan. On the oscillatory and monotone solutions of ordinary differential equations. Archivum Mathematicum, Tome 014 (1978) pp. 21-44. http://gdmltest.u-ga.fr/item/106988/
On the solution of the second order ordinary non-linear equation, (Russian), Dokl. Akad. Nauk Uz. SSR, 1970, N7, 6-8. (1970) | MR 0379935
Method of "standard" equations (VKB-method) for second order non-linear equations, (Russian), Izv. Akad. Nauk Uz. SSR ser. fyz.-mat. nauk, 1970, N4, 3-7. (1970) | MR 0294793
On second-order non-linear oscillations, Pacif. J. Math., 1955, 5, N1, 643-647. (1955) | MR 0072316 | Zbl 0065.32001
Stability theory of differential equations, New York, Mc Graw-Hill, 1953, (1953) | MR 0061235 | Zbl 0053.24705
Oscilatorické riešenia istej nelineárnej diferenciálnej rovnice druhého rádu, Mat.-Fyz. Časopis SAV, 1961, 11, N4, 250-255. (1961)
Neoscilatorické riešenia istej nelineárnej diferenciálnej rovnice druhého rádu, Mat.-Fyz. Časopis SAV, 1962, 12, N4, 253-262. (1962) | MR 0159994
On some properties of the equation $y"(x) + f(x) y^{\alpha}(x) = 0, 0 < \alpha < 1$, Mat. Časopis, 1967, 17, N1, 10-19. (1967) | MR 0214854
Two remarks on the properties of solutìons of a nonlinear differential equation, Acta F. R. N. Univ. Cоmen. - Mathematica, 1969, 22, 19-26. (1969) | MR 0289855
A criterion for oscillation and nonoscillation, Аcta F. R. N. Univ. Cоmen. - Mathematica, 1969, 20, 75-79. (1969) | MR 0274855 | Zbl 0225.34019
Monotone and oscillatory solutions of a class of nonlinear differential equations, Mat. Časоpis, 1969, 19, NЗ. 169-187. (1969) | MR 0304773 | Zbl 0271.34045
O pewnych wlastnościah rozviazan równania rôzniczkowego nieliniowego trzeciego rzedu, Pоznan, Pоlitechnika Pоznanska Rоzprawy, 1967, N24. (1967)
Oscillation theorems for a non-linear analogue of Hill's equation, Quart. J. Math., 1976, 27, N106, 159-171. (1976) | MR 0409976
On the continuation of solutions of a certain non-linear differential equation, Mоnatshefte für Math., 1967, 71, 5, 385-392. (1967) | MR 0227494
On a second order nonlinear oscillation problem, Тrans. Аmer. Math. Sоc., 1970, 147, N2, 357-366. (1970) | MR 0257473
On the existence of oscillatory solutions to nonlinear differential equations, Ann. mat. pura ed appl, 1976, N109, 23-38. (1976) | MR 0481254 | Zbl 0345.34022
Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc., 1918, 19, 341-352. (1918) | MR 1501107
On the solutions of linear second-order differential equations, Proc. Nat. Acad. Sci. U.S.A., 1965, 53, N2, 247-249. (1965) | MR 0174817 | Zbl 0133.34103
The existence of large or small solutions of linear differential equations, Duke Math. J., 1961, 28, N3, 421-429. (1961) | MR 0130432 | Zbl 0102.30301
Boundary value problems in one differential equation with a discontinuity, J. Different. Equat., 1965, 1, N2, 346-369. (1965) | MR 0180723 | Zbl 0142.06303
Uniqueness, continuation, and nonoscillation for a second order nonlinear differential equation, Pacif. J. Math., 1970, 32, N3, 715-721. (1970) | MR 0259244 | Zbl 0188.14301
The existence of oscillatory solutions for a nonlinear odd order differential equation, Czechoslov. Math. J., 1970, 20, N1, 93-97. (1970) | MR 0257468 | Zbl 0183.36902
Oscillatory solutions for a generalized sublinear second order differential equation, Proc. Amer. Math. Soc., 1973, 38, N1, 80-82. (1973) | MR 0310339 | Zbl 0242.34035
Some stability conditions for a nonlinear differential equation, Trans. Amer. Math. Soc., 1969, 139, 349-358. (1969) | MR 0241767 | Zbl 0182.11902
On the conditions of oscillation and non-oscillation of second order non-linear differential equations, (Russian), Differenciaľnye Uravnenija, 1966, 2, N12, 1572-1585. (1966) | MR 0209579
A note on oscillation of solutions of second order non-linear differential equations, Soobšč. Akad. Nauk Gr. SSR, 1967, 57, N1, 19-24. (1967) | MR 0219809
On asymptotic behaviour of solutions of some second order ordinary non-linear differential equations, (Russian), Trudy Tbilis. Gos. Univ., ser. mek.-mat. nauk, 1968, 129, 157-178. (1968) | MR 0255923
On oscillatory solutions of second-order non-linear differential inequalities, Studies of certain equations of mathematical physics (Russian), Tbilisi, Tbilisi Univ. Press, 1972, 17-22. (1972) | MR 0361276
Concerning the oscillation of solutions of second order non-linear differential inequalities and equations, Studies of certain equations of mathematical physycs (Russian), Tbilisi, Tbilisi Univ. Press, 1976, 63-70. (1976) | MR 0594801
Some notes on solutions of the equation $u" + a(t) f(u) = 0$, (Russian), Differenciaľnye Uravnenija, 1968, 4, N4, 589-605. (1968) | MR 0227544
On the existence of an oscillatory solution of the nonlinear differential equation of the second order $y" + f(x) y^{2n-1} = 0, f(x) > 0$, Časopis Pěst. mat., 1960, 85, N1, 78-83. (1960) | MR 0142840
On oscillation of solutions of second order non-linear equation with coefficient with alternating signs, Differentiaľnye Uravnenija, 1970, 6, N9, 1718-1721. (1970) | MR 0277817
On n-th order differential inequalities, J. Math. Anal. Appl., 1975, 52, N1, 1-9. (1975) | MR 0390369 | Zbl 0327.34012
On the conditions of oscillation of solutions of the equation $u" + + a(t) | u |^n \sign u = 0$, (Russian), Časopis Pěst. Mat., 1962, 87, N3, 492-495. (1962) | MR 0181800
On oscillation of solutions of some ordinary differential equations, (Russian), Dokl. Akad. Nauk SSSR, 1962, 144, N1, 33-36. (1962)
On asymptotic properties of solutions of the equation $u" + a(t) | u |^n \sign u = 0$, (Russian), Soobšč. Akad. Nauk Gr. SSR, 1963, 30, N2, 129-136. (1963) | MR 0150385
On non-oscillatory solutions of the equation $u" + a(t) | u |^n \sign u = 0$, (Russian), Soobšč. Akad. Nauk Gr. SSR, 1964, 35, N1, 15-22. (1964) | MR 0166446
Concerning the oscillation of solutions of the equation $\frac{d^m u}{dt^m} + a(t) | u |^n \sign u = 0$, (Russian), Mat. Sb., 1964, 65, N2, 172-187. (1964) | Zbl 0135.14302
The problem of oscillation of solutions of non-linear differential equations, (Russian), Differentiaľnye Uravnenija, 1965, 1, N8, 995-1006. (1965) | MR 0196185
A note on boundedness of solutions of differential equations, (Russian), Trudy Tbilissk. Univ., 1965, 110, 103-108. (1965) | MR 0208089
Asymptotic properties of a certain non-linear differential equation of Emden-Fowler type, (Russian), Izv. Akad. Nauk SSSR, ser. mat., 1965, 29, N5, 965-986. (1965) | MR 0190459
A note on oscillation of solutions of the equation $u" + a(t) | u |^n \sign u = 0$, (Russian), Časopis Pěst. Mat., 1967, 92, N3, 343-350. (1967) | MR 0221012
On monotone solutions of non-linear ordinary differential equations of order n, (Russian), Izv. Akad. Nauk SSSR, ser. mat., 1969, 33, N , 1373-1398. (1969) | MR 0259212
On conditions of oscillation of solutions of non-lineary differential equations, (Russian), I, Differenciaľnye Uravnenija 1974, 10, N8, 1387-1399, II ibidum 1974, 10, N9, 1586-1594. (1974) | MR 0364755
Some singular boundary value problems for ordinary differential equations, Tbilisi, Tbilisi Univ. Press, 1975. (1975) | MR 0499402
A note on asymptotic behaviour of solutions of the equation $u" + a(t)u = 0$, (Russian), Differentiaľnye Uravnenija, 1970, 6, N6, 1115-1117. (1970) | MR 0271481
Local behaviour of solutions of ordinary differential equations, Differentiaľnye Uravnenija, 1971, 7, N8, 1393-1397. (1971) | MR 0288362
Some theorems on boundedness of solutions of ordinary differential equations, Uspechi Mat. Nauk, 1958, 80, N2, 189-194. (1958) | MR 0096029
Untersuchungen über die reellen Nultstellen der Integrate linearer Differentialgleichungen, Math. Ann., 1893, 42, N3, 409-435. | MR 1510784
On oscillation of solutions of linear third and fourth order differential equations, (Russian), Trudy Mosk. Mat. Obšč., 1959, 8, 259-281. (1959) | MR 0104877
On oscillation of solutions of the equation $y" + p(x) y = 0$, (Russian), Trudy Mosk. Mat. Obšč., 1961, 10,419-436. (1961) | MR 0141842
On oscillation of solutions of first order non-linear differential equations with retarded argument, (Russian), Soobšč. Akad. Nauk Gr. SSR, 1973, 70, N1, 17-20. (1973) | MR 0361369
On existence of oscillatory solutions of second order non-linear differential equations with retarded argument, Dokl. Akad. Nauk SSSR, 1973, 210, N2, 260-262. (1973) | MR 0320481
A note on oscillation of solutions of high order differential inequalities and equations with retarded argument, (Russian), DifFerenciaľnye Uravnenija, 1974, 10, N8, 1400-1405. (1974) | MR 0358026
On some properties of the solutions of non-linear differential inequalities and equations with retarded argument, (Russian), Differentiaľnye Uravnenija, 1976, 12, N11, 1971-1984. (1976) | MR 0466843
On oscillatory solutions of functional-differential equations, (Russian), Tbilisi, Tbilisi Univ. Press, 1977. (1977)
On asymptotic behaviour of continued solutions of the equation of Emden-Fowler type, (Russian), Dokl. Akad. Nauk SSSR, 1971, 200, N1, 28-31. d2Y (1971) | MR 0296437
The existence of oscillatory solutions for the equation $\frac{d^2 y}{dt^2} a(t) y^{\tau} =0, 0< \tau< 1$, Proc. Arner. Math. Soc., 1972, 35, 120-122. (1972) | MR 0301292
Sur l'équation $\ddot{x} + f(t) x = 0$, Časopis Pěst. Mat., 1957, 82, N2, 218-226. (1957) | MR 0094506
A note on oscillatory solutions of the equation $y" + f(x) y^{2n-1} = 0$, (Russian), Časop. pro Pěstov. Mat., 1960, 85, N3, 357-358. (1960) | MR 0126025
Oscillatory and asymptotic behaviour of sublinear retarded differential equations, Hiroshima Math. J., 1974, 4, N2, 343-353. (1974) | MR 0350154
Some notes on solutions of Kneser's problem, (Russian), Differenciaľnye Uravnenija, (to appear).
Oscillations of functional-differential equations generated by delays, J. Different. Equat. 1972, 12, N2, 385-395. (1972) | MR 0333399 | Zbl 0227.34053
Oscillations of higher-order retarded differential equations generated by the retarded argument, Delay and Functional Different Equat. and their Appl., New York, Acad. Press, 1972, 219-231. (1972) | MR 0387776 | Zbl 0273.34052
Le caractère oscillatoire des solutions de l'équation $y^{(n)} + f(x) y^{\alpha} = 0$, n> 1, Czechoslov. Math. J., 1963, 13, N4, 481-491. (1963) | MR 0161001
On oscillation and monotonicity of solutions of non-linear differential equations with retarded argument, (Russian), Math. Slov., 1976, 26, N2, 139-152. (1976) | MR 0466867
On Fite's oscillation theorems, Coiloq. Math., 1949, 2, N1, 34-39. (1949) | MR 0041307 | Zbl 0039.31302
Sur l'équation différentielle $x" + A(t) x = 0$, Prace Mat. Fizy., 1934, 41, 39-54 (1934)
Concerning oscillation of solutions of a system of non-linear differential equations, (Russian), Mat. Zametki, 1974, 16, N4, 571-576. (1974) | MR 0374562
On certain asymptotic properties of solutions of two-dimensional differential systems, Soobšč. Akad. Nauk Gr. SSR, 1975, 80, N3, 545-548. (1975) | MR 0407378
On the analogue of Kurzweil-Jasny's theorem for the system of two differential equations, (Russian), Časopis Pěst. Mat., 1976, 101, N1, 45-52. (1976) | MR 0450679
Some notes on asymptotic behaviour of solutions of two-dimensional non-linear differential systems, Studies of certain equations of mathematical physics (Russian) Tbilisi, Tbilisi Univ. Press, 1976, 131-153. (1976)
On the progress of the theory of oscillation of solutions of differential equations with retarded argument, (Russian), Ukr. Mat. Ž., 1977, 29, N3, 313-323. (1977)
The example of the solution of oscillatory type of the second order differential equation which can't be continued to the whole axis, (Russian), Differenciaľnye Uravnenija, 1969, 5, N12, 2667-2668. (1969)
Oscillation of differential inequalities with retarded arguments, Hiroshima Math. J., 1975, 5, N2, 187-192. (1975) | MR 0374614
A nonlinear oscillation problem, J. Different. Equat., 1969, 5, N3, 452-460. (1969) | MR 0235203 | Zbl 0181.09702
On one comparison theorem for the system of two differential equations, (Russian), Differenciaľnye Uravnenija, 1977, 13, N7, 1336-1338. (1977) | MR 0499444
On asymptotic behaviour of solutions of linear differential equations, (Russian), Dokl. Akad. Nauk SSSR, 1948, 61, N2, 219-222. (1948) | MR 0025650
Sur une propriété des intégrales de l'equation $y^{(n)} + Q(x) y = 0, n = 3, 4$, Czechoslov. Math. J., 1957, 7, 450-462. (1957) | MR 0095313
On certain properties of solutions of delay differential equations, (Russian), Ukr. Mat. Ž., 1972, 24, N6, 807-814. (1972)
An oscillation criterion for a nonlinear second order equation, J. Math. Anal. Appl., 1965, 10, N2, 439-441. (1965) | MR 0173050 | Zbl 0131.08902
On asymptotic representation of solutions of the equation $u" = a(t) | u |^n \sign u$, (Russian), Differenciaľnye Uravnenija, 1972, 8, N7, 1195-1206. (1972) | MR 0306638
On asymptotic representation of oscillatory solutions of the perturbed equation of Emden-Fowler type, Studies of certain equations of mathematical physics (Russian), Tbilisi, Tbilisi Univ. Press, 1972, 5-15. (1972)
On asymptotic behaviour of oscillatory solutions of second order ordinary differential equations, (Russian), Differenciaľnye Uravnenija, 1975, 11, N7, 1232-1245. (1975) | MR 0377179
On singular solutions of nonlinear systems of ordinary differential equations, Coll. Math. Soc. János Bolyai, 15. Different. Equat., Keszthely (Hungary), 1975, 107-119. (1975) | MR 0591720
On one comparison theorem for linear differential equations, (Russian), Izv. Akad. Nauk SSSR, ser. mat., 1976, 40, N5, 1128-1142. (1976) | MR 0432973
On singular solutions of strongly nonlinear systems of ordinary equations, Funct. Theoretic Methods in Different. Equat., London, Pitman Publ., 1976, 196-204. (1976) | MR 0477225
Some notes on oscillation of solutions of differential equations with retarded argument, Differenciaľnye Uravnenija (to appear).
Kriterien für die Oszillation der Lösungen der Differentialgleichung $(p(x) y')' + q(x) y = 0$, Časopis Pěst. Mat., 1959, 84, No 3, 335-370. (1959) | MR 0114964
Asymptotische Formeln für die Lösungen der Differentialgleichung $y" + q(x) y = 0$, Čechoslov. mat. žurnal 1964, 14 (89), 203-221. (1964) | MR 0165173
Les développements asymptotiques des solutions de l'équation $(py')' + qy = 0$, Arch. Math., 2, (1966), 1-17. (1966) | MR 0199488