Periodic solutions of Liénard equations
Rendiconti del Seminario Matematico della Università di Padova, Tome 72 (1984), pp. 203-230. 
@article{RSMUP_1984__72__203_0,
     author = {Omari, Pierpaolo and Zanolin, Fabio},
     title = {Periodic solutions of {Li\'enard} equations},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {203--230},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {72},
     year = {1984},
     mrnumber = {778342},
     zbl = {0584.34045},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1984__72__203_0/}
}
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Omari, Pierpaolo; Zanolin, Fabio. Periodic solutions of Liénard equations. Rendiconti del Seminario Matematico della Università di Padova, Tome 72 (1984), pp. 203-230. http://www.numdam.org/item/RSMUP_1984__72__203_0/

[1] J.W. Bebernes - M. MARTELLI, Periodic solutions for Liénard systems, Boll. Un. Mat. Ital., (5) 16-A, (1979), pp. 398-405. | MR | Zbl

[2] J.W. Bebernes - M. Martelli, On the structure of the solution set for periodic boundary value problems, J. Nonlinear Anal., TMA, 4 (4), (1980), pp. 821-830. | MR | Zbl

[3] H. Brézis - L. Nirenberg, Characterizations of the range of some nonlinear operators and applications to boundary value problems, Annali Scuola Norm. Sup. Pisa, C. Sci. (4), 5 (2) (1978), pp. 225-326. | Numdam | MR | Zbl

[4] M.L. Cartwright - J.E. Littlewood, On nonlinear differential equations of the second order, Ann. of Math., 48 (1947), pp. 472-494. | MR | Zbl

[5] L. Cesari - R. KANNAN, Solutions in the large of Liénard equations with forcing terms, Ann. Mat. Pura Appl., 111 (1976), pp. 101-124. | MR | Zbl

[6] L. Cesari - R. KANNAN, Periodic solutions in the large of Liénard systems with forcing terms, Boll. Un. Mat. Ital. (6), 1-A, (1982), pp. 217-224. | MR | Zbl

[7] R.E. Gaines - J. Mawhin, Coincidence degree and nonlinear differential equations, Lecture Notes in Math., 568, Springer-Verlag, Berlin and New York (1977). | MR | Zbl

[8] R. Gomory, Critical points at infinity and forced oscillations, Contrib. Theory Nonlinear Oscill., 3, Ann. of Math. Stud. n° 36, Princeton (1965), pp. 85-126. | MR | Zbl

[9] R.B. Grafton, Periodic solutions of Liénard equations with delay: some theoretical and numerical results, in Delay and functional differential equations and their applications (Proc. Conf. Park. City, Utah, 1972), K. Schmitt, Ed., Academic Press, New York (1972), pp. 321-334. | MR | Zbl

[10] M.A. Krasnosel'Skii, The operator of translation along the trajectories of differential equations, Transl. Math. Monographs, 19, Amer. Math. Soc., Providence, R.I. (1968). | MR

[11] J. La SALLE - S. LEFSCHETZ, Stability by Liapunov's direct method, with applications, Academic Press, New York (1961). | MR | Zbl

[12] S. Lefschetz, Existence of periodic solutions for certain differential equations, Proc. Nat. Acad. Sci. USA, 29 (1943), pp. 29-32. | MR | Zbl

[13] N. Levinson, On the existence of periodic solutions for second order differential equations with a forcing term, Jour. Math. Phis., 22 (1943), pp. 41-48. | MR | Zbl

[14] L. Marcus, Lectures in differentiable dynamics, Regional Conference Series in Mathematics, CBMS, 3 (1971). | MR | Zbl

[15] J. Mawhin, Degré topologique et solutions périodiques des systémes différentiels nonlineaires, Bull. Soc. Roy. Sci. Liége, 38 (1969), pp. 308-398. | MR | Zbl

[16] J. Mawhin, Equations intégrales et solutions périodiques des systémes différentiels non linéaires, Acad. Roy. Belg. Bull. Cl. Sci. (5), 55 (1969), pp. 934-947. | MR | Zbl

[17] J. Mawhin, Periodic solutions of strongly nonlinear differential systems, in Proo. Fifth Intern. Conf. Nonlinear Oscill., Izd. Inst. Mat. Akad. Nauk. Ukr. S.S.R., Kiev, 1 (1970), pp. 380-400. | MR | Zbl

[18] J. Mawhin, Periodic solutions of nonlinear functional differential equations, J. Differential Equations, 10 (1971), pp. 240-261. | MR | Zbl

[19] J. Mawhin, An extension of a theorem of A. C. Lazer on forced nonlinear osoillations, J. Math. Anal. Appl., 40 (1972), pp. 20-29. | MR | Zbl

[20] J. Mawhin, Topological degree methods in nonlinear boundary value problems, Regional Conference Series in Mathematics, CBMS, 40 (1979). | MR | Zbl

[21] S. Mizohata - S. Yamaguti, On the existence of periodic solutions of the nonlinear differential equations x''+ α(x)x' + ϕ(x) = p(t), Mem. Coll. Sci. Univ. Kyoto, Sec. A, 27 (1952), pp. 109-113. | MR | Zbl

[22] M.H.A. Newman, On the ultimate boundedness of the solutions of certain differential equations, Compositio Math., 8 (1951), pp. 142-156. | EuDML | Numdam | MR | Zbl

[23] P. Omari, Periodic solutions of strongly damped Liénard systems with delay, Boll. Un. Mat. Ital., (6) 2-B (1983), pp. 915-927. | MR | Zbl

[24] P. Omari - F. Zanolin, On forced nonlinear oscillations in n-th order differential systems with geometric conditions, J. Nonlinear Anal., TMA (to appear). | MR | Zbl

[25] Z. Opial, Sur les solutions périodiques et presque-périodiques de l'équation différentielle x'' + kf(x)x' + g(x) = kp(t), Ann. Polon. Math., 7 (1959-60), pp. 309-319. | EuDML | MR | Zbl

[26] R. Reissig, Über eine nichtlineare Differentialgleichung 2. Ordnung, Math. Nachrichten, 13 (1955), pp. 313-318. | MR | Zbl

[27] R. Reissig, Continua of periodic solutions of the Liénard equation, in Constructive methods for nonlinear boundary value problems and nonlinear oscillations, Conf. Oberwolfach 1978, ISNM, 48 (1979), pp. 126-133. | MR | Zbl

[28] R. Reissig - G. Sansone - R. Conti, Qualitative Theorie nichtlinearer Differentialgleichungen, Cremonese, Roma (1963). | MR | Zbl

[29] G.E.H. Reuter, A boundedness theorem for nonlinear differential equations of the second order, Proc. Cambr. Phil. Soc., 47 (1951), pp. 49-54. | MR | Zbl

[30] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970). | MR | Zbl

[31] M. Roseau, Solutions périodiques ou presque périodiques des systèmes différentiels de la méoanique non linéaire, CISM Courses and Lectures n. 44, Udine (1970). | Zbl

[32] N. Rouche - J. Mawhin, Equations différentielles ordinaires, (2 volumes), Masson, Paris (1973). | MR

[33] G. Sansone - R. Conti, Equazioni differenziali non lineari, Cremonese, Roma (1956). | MR | Zbl

[34] J.J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscence Publ., Inc., New York (1950). | MR | Zbl

[35] J.R. Wardjr., Periodic solutions of a ctass of ordinary differential equations, Proc. Amer. Math. Soc., 78 (1980), pp. 350-352. | MR | Zbl

[36] T. Yoshizawa, Stability theory by Liapunov's second method, The Math. Soc. of Japan, Tokyo (1966). | MR | Zbl

[37] F. Zanolin, On forced nonlinear oscittations for some second order delay-differential systems, in Evolution equations and their applications (Proc. Conf. Diff. Equations and Appl., Retzhof, 1981), F. Kappel and W. Shappacher, Ed., Researches Notes in Mathematics, 68, Pitman, Boston (1982), pp. 295-313. | MR | Zbl

[38] F. Zanolin, On forced periodic oscillations in dissipative Liénard Systems, Rend. Sem. Mat. Univ. Padova, 69, (1982), pp. 51-62. | EuDML | Numdam | MR | Zbl