Forced vibrations of wave equations with non-monotone nonlinearities
Berti, Massimiliano ; Biasco, Luca
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 439-474 / Harvested from Numdam
@article{AIHPC_2006__23_4_439_0,
     author = {Berti, Massimiliano and Biasco, Luca},
     title = {Forced vibrations of wave equations with non-monotone nonlinearities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {439-474},
     doi = {10.1016/j.anihpc.2005.05.004},
     mrnumber = {2245752},
     zbl = {1103.35076},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_4_439_0}
}
Berti, Massimiliano; Biasco, Luca. Forced vibrations of wave equations with non-monotone nonlinearities. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 439-474. doi : 10.1016/j.anihpc.2005.05.004. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_4_439_0/

[1] A. Ambrosetti, A. Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on R n , Birkhäuser, in press. | MR 2186962 | Zbl 05013399

[2] Bambusi D., Paleari S., Families of periodic solutions of resonant PDEs, J. Nonlinear Sci. 11 (1) (2001) 69-87. | MR 1819863 | Zbl 0994.37040

[3] Bartsch T., Ding Y.H., Lee C., Periodic solutions of a wave equation with concave and convex nonlinearities, J. Differential Equations 153 (1) (1999) 121-141. | MR 1682275 | Zbl 0926.35013

[4] Berti M., Biasco L., Periodic solutions of nonlinear wave equations with non-monotone forcing terms, Rend. Mat. Acc. Naz. Lincei, s. 9 16 (2) (2005) 109-116. | MR 2225505 | Zbl 05058571

[5] Berti M., Bolle P., Periodic solutions of nonlinear wave equations with general nonlinearities, Comm. Math. Phys. 243 (2) (2003) 315-328. | MR 2021909 | Zbl 1072.35015

[6] Berti M., Bolle P., Multiplicity of periodic solutions of nonlinear wave equations, Nonlinear Anal. 56 (2004) 1011-1046. | MR 2038735 | Zbl 1064.35119

[7] M. Berti, P. Bolle, Cantor families of periodic solution for completely resonant wave equations, Preprint SISSA, 2004. | MR 2072952

[8] Bourgain J., Periodic solutions of nonlinear wave equations, in: Harmonic Analysis and Partial Differential Equations, Chicago Lectures in Math., Univ. Chicago Press, 1999, pp. 69-97. | MR 1743856 | Zbl 0976.35041

[9] Brézis H., Coron J.-M., Nirenberg L., Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure Appl. Math. 33 (5) (1980) 667-684. | MR 586417 | Zbl 0484.35057

[10] Brézis H., Nirenberg L., Forced vibrations for a nonlinear wave equation, Comm. Pure Appl. Math. 31 (1) (1978) 1-30. | MR 470377 | Zbl 0378.35040

[11] Coron J.-M., Periodic solutions of a nonlinear wave equation without assumption of monotonicity, Math. Ann. 262 (2) (1983) 273-285. | MR 690201 | Zbl 0489.35061

[12] De Simon L., Torelli H., Soluzioni periodiche di equazioni a derivate parziali di tipo iperbolico non lineari, Rend. Sem. Mat. Univ. Padova 40 (1968) 380-401. | Numdam | MR 228836 | Zbl 0198.13704

[13] Gentile G., Mastropietro V., Procesi M., Periodic solutions for completely resonant nonlinear wave equations, Comm. Math. Phys. 256 (2005) 437-490. | MR 2160800 | Zbl 1094.35021

[14] Hall W.S., On the existence of periodic solutions for the equations D tt u+(-1) p 0ex0exD x 2p u=ϵf(·,·,u), J. Differential Equations 7 (1970) 509-526. | MR 265738 | Zbl 0198.14002

[15] Hofer H., On the range of a wave operator with non-monotone nonlinearity, Math. Nachr. 106 (1982) 327-340. | MR 675766 | Zbl 0505.35058

[16] Lovicarová H., Periodic solutions of a weakly nonlinear wave equation in one dimension, Czechoslovak Math. J. 19 (94) (1969) 324-342. | MR 247249 | Zbl 0181.10901

[17] Plotnikov P.I., Yungerman L.N., Periodic solutions of a weakly nonlinear wave equation with an irrational relation of period to interval length, Differentsial'nye Uravneniya 24 (9) (1988) 1599-1607, 1654 (in Russian); Translation in, Differential Equations 24 (9) (1988) 1059-1065, (1989). | MR 965608 | Zbl 0675.35058

[18] Rabinowitz P., Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math. 20 (1967) 145-205. | MR 206507 | Zbl 0152.10003

[19] Rabinowitz P., Time periodic solutions of nonlinear wave equations, Manuscripta Math. 5 (1971) 165-194. | MR 326179 | Zbl 0219.35062

[20] Torelli G., Soluzioni periodiche dell’equazione non lineare u tt -u xx +ϵF(x,t,u)=0, Rend. Istit. Mat. Univ. Trieste 1 (1969) 123-137. | MR 271520 | Zbl 0186.42903

[21] Willem M., Density of the range of potential operators, Proc. Amer. Math. Soc. 83 (2) (1981) 341-344. | MR 624926 | Zbl 0478.49012