Forced vibrations of wave equations with non-monotone nonlinearities

Berti, Massimiliano; Biasco, Luca

doi:10.1016/j.anihpc.2005.05.004

Berti, Massimiliano ; Biasco, Luca

Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 4, pp. 439-474.

MR Zbl

DOI : 10.1016/j.anihpc.2005.05.004

@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},
     pages = {439--474},
     publisher = {Elsevier},
     volume = {23},
     number = {4},
     year = {2006},
     doi = {10.1016/j.anihpc.2005.05.004},
     mrnumber = {2245752},
     zbl = {1103.35076},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2005.05.004/}
}

TY  - JOUR
AU  - Berti, Massimiliano
AU  - Biasco, Luca
TI  - Forced vibrations of wave equations with non-monotone nonlinearities
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2006
SP  - 439
EP  - 474
VL  - 23
IS  - 4
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2005.05.004/
DO  - 10.1016/j.anihpc.2005.05.004
LA  - en
ID  - AIHPC_2006__23_4_439_0
ER  -

%0 Journal Article
%A Berti, Massimiliano
%A Biasco, Luca
%T Forced vibrations of wave equations with non-monotone nonlinearities
%J Annales de l'I.H.P. Analyse non linéaire
%D 2006
%P 439-474
%V 23
%N 4
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2005.05.004/
%R 10.1016/j.anihpc.2005.05.004
%G en
%F 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) no. 4, pp. 439-474. doi : 10.1016/j.anihpc.2005.05.004. https://www.numdam.org/articles/10.1016/j.anihpc.2005.05.004/

Bibliographie
Cité par

[1] A. Ambrosetti, A. Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on $R^{n}$ , Birkhäuser, in press. | MR | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

[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 | Zbl

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

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

[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. | EuDML | Numdam | MR | Zbl

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

[14] Hall W.S., On the existence of periodic solutions for the equations $D_{t t} u + {(- 1)}^{p} {D_{x}}^{2 p} u = ϵ f (\cdot, \cdot, u)$ , J. Differential Equations 7 (1970) 509-526. | MR | Zbl

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

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

[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 | Zbl

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

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

[20] Torelli G., Soluzioni periodiche dell’equazione non lineare $u_{t t} - u_{x x} + ϵ F (x, t, u) = 0$ , Rend. Istit. Mat. Univ. Trieste 1 (1969) 123-137. | MR | Zbl

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

CAI, AO; LV, HUIHUI; WANG, ZHIGUO Quantitative reducibility of $C^{k}$ quasi-periodic cocycles, Ergodic Theory and Dynamical Systems (2024), p. 1 | DOI:10.1017/etds.2024.88
Ji, Shuguan; Rudakov, Igor A. Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends, Calculus of Variations and Partial Differential Equations, Volume 62 (2023) no. 2 | DOI:10.1007/s00526-022-02404-3
曾, 燕苗 Time Periodic Solutions of Nonlinear Waveequation with Dirichletboundary Conditions, Pure Mathematics, Volume 13 (2023) no. 04, p. 1142 | DOI:10.12677/pm.2023.134119
Cai, Ao The Absolutely Continuous Spectrum of Finitely Differentiable Quasi-Periodic Schrödinger Operators, Annales Henri Poincaré, Volume 23 (2022) no. 12, p. 4195 | DOI:10.1007/s00023-022-01192-y
Li, Long; Damanik, David; Zhou, Qi Cantor spectrum for CMV matrices with almost periodic Verblunsky coefficients, Journal of Functional Analysis, Volume 283 (2022) no. 12, p. 109709 | DOI:10.1016/j.jfa.2022.109709
Ji, Shuguan Periodic solutions of two-dimensional wave equations with x-dependent coefficients and Sturm–Liouville boundary conditions, Nonlinearity, Volume 35 (2022) no. 10, p. 5033 | DOI:10.1088/1361-6544/ac8217
Li, Xianzhe Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications, Nonlinearity, Volume 35 (2022) no. 12, p. 6124 | DOI:10.1088/1361-6544/ac98ed
Caicedo, Jose F.; Castro, Alfonso; Duque, Rodrigo A semilinear wave equation with non-monotone nonlinearity and forcing flat on characteristics, Electronic Journal of Differential Equations (2021) no. Special Issue 01, p. 91 | DOI:10.58997/ejde.sp.01.c1
Rudakov, I. A. Problem on Periodic Vibrations of an I-beam with Clamped Endpoint in the Resonance Case, Differential Equations, Volume 56 (2020) no. 3, p. 330 | DOI:10.1134/s0012266120030064
Rudakov, I.A. Oscillation Problem for an I-Beam with Fixed and Hinged End Supports, Herald of the Bauman Moscow State Technical University. Series Natural Sciences (2019) no. 84, p. 4 | DOI:10.18698/1812-3368-2019-3-4-21
Cai, Ao; Chavaudret, Claire; You, Jiangong; Zhou, Qi Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles, Mathematische Zeitschrift, Volume 291 (2019) no. 3-4, p. 931 | DOI:10.1007/s00209-018-2147-5
Nowakowski, Andrzej; Rogowski, Andrzej Wave equation in higher dimensions - periodic solutions, Electronic Journal of Qualitative Theory of Differential Equations (2018) no. 103, p. 1 | DOI:10.14232/ejqtde.2018.1.103
Ji, Shuguan Periodic solutions for one dimensional wave equation with bounded nonlinearity, Journal of Differential Equations, Volume 264 (2018) no. 9, p. 5527 | DOI:10.1016/j.jde.2018.02.001
Rui, Jie; Liu, Bingchen Almost-periodic solutions of an almost-periodically forced wave equation, Journal of Mathematical Analysis and Applications, Volume 451 (2017) no. 2, p. 629 | DOI:10.1016/j.jmaa.2017.02.036
Nowakowski, Andrzej; O'regan, Donal Periodic Navier Solutions for the Plate Equation with Non-Monotone Nonlinearities: the Multidimensional Case, Proceedings of the Edinburgh Mathematical Society, Volume 60 (2017) no. 1, p. 203 | DOI:10.1017/s0013091516000092
Nowakowski, Andrzej; O’Regan, Donal Periodic solutions for forced vibrations of wave equation with general nonlinearities: the multidimensional case, Applicable Analysis, Volume 94 (2015) no. 2, p. 399 | DOI:10.1080/00036811.2014.898270
Caicedo, José; Castro, Alfonso; Duque, Rodrigo; Sanjuán, Arturo Existence of $L^{p}$ -solutions for a semilinear wave equation with non-monotone nonlinearity, Discrete Continuous Dynamical Systems - S, Volume 7 (2014) no. 6, p. 1193 | DOI:10.3934/dcdss.2014.7.1193
You, Jiangong; Zhou, Qi Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications, Communications in Mathematical Physics, Volume 323 (2013) no. 3, p. 975 | DOI:10.1007/s00220-013-1800-4
Si, Jianguo Quasi-periodic solutions of a non-autonomous wave equations with quasi-periodic forcing, Journal of Differential Equations, Volume 252 (2012) no. 10, p. 5274 | DOI:10.1016/j.jde.2012.01.034
Ji, Shuguan; Li, Yong Time Periodic Solutions to the One-Dimensional Nonlinear Wave Equation, Archive for Rational Mechanics and Analysis, Volume 199 (2011) no. 2, p. 435 | DOI:10.1007/s00205-010-0328-4
Caicedo, José F.; Castro, Alfonso; Duque, Rodrigo Existence of Solutions for a Wave Equation with Non-monotone Nonlinearity and a Small Parameter, Milan Journal of Mathematics, Volume 79 (2011) no. 1, p. 207 | DOI:10.1007/s00032-011-0154-7
Ji, Shuguan Periodic solutions on the Sturm–Liouville boundary value problem for two-dimensional wave equation, Journal of Mathematical Physics, Volume 50 (2009) no. 11 | DOI:10.1063/1.3255567
Ji, Shuguan Time-periodic solutions to a nonlinear wave equation with periodic or anti-periodic boundary conditions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 465 (2009) no. 2103, p. 895 | DOI:10.1098/rspa.2008.0272
Baldi, Pietro; Berti, Massimiliano Forced Vibrations of a Nonhomogeneous String, SIAM Journal on Mathematical Analysis, Volume 40 (2008) no. 1, p. 382 | DOI:10.1137/060665038

Cité par 24 documents. Sources : Crossref