Periodic solutions of Liénard equations

 Access to full text

 Full (PDF)

1. [1] J.W. Bebernes - M. MARTELLI, Periodic solutions for Liénard systems, Boll. Un. Mat. Ital., (5) 16-A, (1979), pp. 398-405. Zbl0425.34044MR541782
2. [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. Zbl0453.34019MR582550
3. [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. Zbl0386.47035MR513090
4. [4] M.L. Cartwright - J.E. Littlewood, On nonlinear differential equations of the second order, Ann. of Math., 48 (1947), pp. 472-494. Zbl0029.12602MR21190
5. [5] L. Cesari - R. KANNAN, Solutions in the large of Liénard equations with forcing terms, Ann. Mat. Pura Appl., 111 (1976), pp. 101-124. Zbl0429.34038MR427751
6. [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. Zbl0492.34030MR663284
7. [7] R.E. Gaines - J. Mawhin, Coincidence degree and nonlinear differential equations, Lecture Notes in Math., 568, Springer-Verlag, Berlin and New York (1977). Zbl0339.47031MR637067
8. [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. Zbl0071.08801MR85414
9. [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. Zbl0275.34069MR387775
10. [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). MR223640
11. [11] J. LaSALLE - S. LEFSCHETZ, Stability by Liapunov's direct method, with applications, Academic Press, New York (1961). Zbl0098.06102MR132876
12. [12] S. Lefschetz, Existence of periodic solutions for certain differential equations, Proc. Nat. Acad. Sci. USA, 29 (1943), pp. 29-32. Zbl0061.19002MR7462
13. [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. Zbl0061.18909MR8866
14. [14] L. Marcus, Lectures in differentiable dynamics, Regional Conference Series in Mathematics, CBMS, 3 (1971). Zbl0214.50701
15. [15] J. Mawhin, Degré topologique et solutions périodiques des systémes différentiels nonlineaires, Bull. Soc. Roy. Sci.Liége, 38 (1969), pp. 308-398. Zbl0186.41704MR594965
16. [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. Zbl0193.06103MR265691
17. [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. Zbl0243.34075MR320444
18. [18] J. Mawhin, Periodic solutions of nonlinear functional differential equations, J. Differential Equations, 10 (1971), pp. 240-261. Zbl0223.34055MR294823
19. [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. Zbl0245.34035MR313587
20. [20] J. Mawhin, Topological degree methods in nonlinear boundary value problems, Regional Conference Series in Mathematics, CBMS, 40 (1979). Zbl0414.34025MR525202
21. [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. Zbl0048.06803
22. [22] M.H.A. Newman, On the ultimate boundedness of the solutions of certain differential equations, Compositio Math., 8 (1951), pp. 142-156. Zbl0039.31201MR39876
23. [23] P. Omari, Periodic solutions of strongly damped Liénard systems with delay, Boll. Un. Mat. Ital., (6) 2-B (1983), pp. 915-927. Zbl0532.34048MR737443
24. [24] P. Omari - F. Zanolin, On forced nonlinear oscillations in n-th order differential systems with geometric conditions, J. Nonlinear Anal., TMA (to appear). Zbl0542.34037MR750046
25. [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. Zbl0092.08703MR114971
26. [26] R. Reissig, Über eine nichtlineare Differentialgleichung 2. Ordnung, Math. Nachrichten, 13 (1955), pp. 313-318. Zbl0067.06701MR70809
27. [27] R. Reissig, Continua of periodic solutions of the Liénard equation, in Constructive methods for nonlinear boundary value problems and nonlinear oscillations, Conf. Oberwolfach1978, ISNM, 48 (1979), pp. 126-133. Zbl0416.34045MR565646
28. [28] R. Reissig - G. Sansone - R. Conti, Qualitative Theorie nichtlinearer Differentialgleichungen, Cremonese, Roma (1963). Zbl0114.04302MR158121
29. [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. Zbl0042.09401MR41306
30. [30] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970). Zbl0193.18401MR274683
31. [31] M. Roseau, Solutions périodiques ou presque périodiques des systèmes différentiels de la méoanique non linéaire, CISM Courses and Lectures n. 44, Udine (1970). Zbl0272.70016
32. [32] N. Rouche - J. Mawhin, Equations différentielles ordinaires, (2 volumes), Masson, Paris (1973). Zbl0289.34001MR481182
33. [33] G. Sansone - R. Conti, Equazioni differenziali non lineari, Cremonese, Roma (1956). Zbl0075.26803MR88607
34. [34] J.J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscence Publ., Inc., New York (1950). Zbl0035.39603MR34932
35. [35] J.R. Wardjr., Periodic solutions of a ctass of ordinary differential equations, Proc. Amer. Math. Soc., 78 (1980), pp. 350-352. Zbl0433.34030
36. [36] T. Yoshizawa, Stability theory by Liapunov's second method, The Math. Soc. of Japan, Tokyo (1966). Zbl0144.10802MR208086
37. [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. Zbl0492.34058MR668394
38. [38] F. Zanolin, On forced periodic oscillations in dissipative Liénard Systems, Rend. Sem. Mat. Univ. Padova, 69, (1982), pp. 51-62. Zbl0522.34041MR716985