@article{PMFA_1994_39_1_a2,
author = {Hrici\v{s}\'akov\'a, Daniela},
title = {Zov\v{s}eobecnen\'a {Li\'enardova} diferenci\'alna rovnica},
journal = {Pokroky matematiky, fyziky a astronomie},
pages = {26--34},
year = {1994},
volume = {39},
number = {1},
mrnumber = {1280449},
zbl = {0808.34044},
language = {sk},
url = {http://geodesic.mathdoc.fr/item/PMFA_1994_39_1_a2/}
}
Hricišáková, Daniela. Zovšeobecnená Liénardova diferenciálna rovnica. Pokroky matematiky, fyziky a astronomie, Tome 39 (1994) no. 1, pp. 26-34. http://geodesic.mathdoc.fr/item/PMFA_1994_39_1_a2/
[1] Bendixon, I.: Sur les courbes définies par des équations differentielles. Acta Math. 24 (1901), 1–88.
[2] Benson, D. C.: Asymptotic directions for solutions of Liénard systems. Nonlinear Anal. Theory Method Appl. 6 (1982), 293–301. | MR | Zbl
[3] Birkhoff, G. D.: Dynamical Systems. Amer. Math. Soc. Coll. Publ., New York 1927.
[4] Cartan, E. H.: Note sur la génération des oscillations entretenues. Ann. Postes Télégraph 14 (1925), 1196–1207.
[5] Cotton, E.: Sur les solutions asymptotiques des équations différentielles. Ann. Sci. École Norm. Sup. 28 (1911), 473–521. | MR
[6] De Figueiredo, R. J. P., Chang, C.-Y.: On the boundedness of solutions of classes of multidimensional nonlinear autonomous systems. SIAM J. Appl. Math. 17 (1969), 672–680. | MR | Zbl
[7] Ding, W.: On the existence of periodic solutions for Liénard systems. Acta Math. Sinica 25 (1982), 626–632. | MR | Zbl
[8] Fučík, Sv., Mawhin, J.: Periodic solutions of some nonlinear equation of higher order. Čas. pěst. mat. 100 (1975), 276–283. | MR
[9] Graef, J. R.: On the generalized Liénard equation with negative damping. J. Differential Equations 12 (1972), 34–62. | MR | Zbl
[10] Hara, T., Yoneyama, T.: On the Global Center of Generalized Liénard Equation and its Application to Stability Problems. Funkcial. Ekvac. 28 (1985), 171–192. | MR | Zbl
[11] Hara, T., Yoneyama, T.: On the Global Center of Generalized Liénard Équation and its Application to Stability Problems II. Funkcial. Ekvac. 31 (1988), 221–225. | MR | Zbl
[12] Hricišáková, D.: Existence of ultimately positive (negative) solutions of generalized Liénard equation. EQUADIFF 7, Praha 1989.
[13] Hricišáková, D.: Continuability and (non)oscilatory properties of solutions of generalized Liénard equation. Hiroshima Math. J. Vol. 20, No. 1., March 1990, 11–22. | MR
[14] Hricišáková, D.: Existence of positive solutions of Liénard differential equation. J. of Mathematical analysis and applications, San Diego, California, Vol. 176, No. 2, July 1, 1993, 545–553.
[15] Lefschetz, S.: Existence of periodic solutions for certain differential equations. Proc. Nat. Acad. Sci. USA 29 (1943), 29–32. | MR | Zbl
[16] Lefschetz, S.: Lectures on differential equations. Ann. Math. Stud. 14, Princeton 1948.
[17] Levi-Civita, T.: Sopra alcuni criteri di instabilita. Ann. Mat. Pura Appl. 5 (1901), 221–301.
[18] Ljapunov, M. A.: Das allgemeine Problem der Stabilität einer Bewegung. Math. Gesselsch. Charkov 1892.
[19] Liénard, A.: Étude des oscillations autoentretenues. Rev. Gén. Élec. 23 (1928), 901–902, 946–954.
[20] Mawhin, J., Everitt, W. N., Sleeman, B. D.: Periodic oscillations of forced pendulum-like equations. In Ordinary and Partial Differential Equations . (W. N. Everitt and B. D. Sleeman, Eds.) Lecture Notes in Mathematics Vol. 924, Springer-Verlag Berlin/New York 1982, 458–476. | MR
[21] Mawhin, J., Willem, M.: Multiple solutions of the periodic boundary value problem for some pendulum-type equations. J. Differential Equations 52 (1984), 264–287. | MR
[22] Minorsky, N.: Nonlinear Oscillations. Van Nostrand, Princeton, NJ, 1962. | MR | Zbl
[23] Mizohata, S., Yamaguti, M.: On the existence of periodic solutions of the nonlinear differential equation $\ddot{x}+\alpha (\dot{x})+Q(x)=p(t)$. Mem. Coll. Sci. Univ. Kyoto Sect. A 27 (1952), 142–156. | MR
[24] Nemickij, V. V., Stepanov, V. V.: Theorie der Differentialgleichungen. Moskva 1949.
[25] Opial, Z.: Sur un théoréme de A. Filippoff. Ann. Polon. Math. 5 (1958), 67–75. | MR | Zbl
[26] Poincaré, H.: Mémoires sur les courbes définies par une équation différentielle. J. Math. Pures Appl. 7 (1881), 375–422, 8 (1882), 251–296, 1 (1885), 167–224, 2 (1886), 151–217.
[27] Poincaré, H.: Les méthodes nouvelles de la mécanique céleste. Paris 1892.
[28] Pol, B. van der: A theory of the amplitude of free and forced triode vibrations. Radio Reviews I (1920), 701–710.
[29] Reissig, R.: Schwingungssätze für die verallgemeinerte Liénardsche Differentialgleichung. Abh. Math. Sem. Univ. Hamburg 44 (1957), 45–51. | MR
[30] Reissig R., Sansone G., Conti R.: Qualitative Theorie Nichtlinearer Differentialgleichungen. Edizioni Cremonese, Roma 1963. | MR
[31] Sansone, G.: Sopra l’equazione di A. Liénard per le oscillazioni di rilassamento. Ann. Mat. Pura Appl. 28 (1949), 153–181. | MR | Zbl
[32] Wu, K.: The existence of limit cycles for a nonlinear system. Acta Math. Sinica 25 (1982), 456–463. | MR | Zbl
[33] Zanolin, F.: Remarks on multiple periodic solutions for nonlinear ordinary differential systems of Liénard type. Boll. Un. Mat. Ital. 8(6) (1982), 683–698. | MR | Zbl
[34] Zeng, X.: An existence and uniqueness theorem of limit cycles of Liénard equation. Acta Math. Sinica 21 (1978), 263–269 (Chinese). | MR | Zbl