| Title:
|
Periodic solutions of the equation $u_{tt}+u_{xxxx}=\varepsilon f(\cdot,\cdot,u,u_t)$ (English) |
| Author:
|
Petzeltová, Hana |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
23 |
| Issue:
|
2 |
| Year:
|
1973 |
| Pages:
|
269-285 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B10 |
| idZBL:
|
Zbl 0263.35017 |
| idMR:
|
MR0328286 |
| DOI:
|
10.21136/CMJ.1973.101166 |
| . |
| Date available:
|
2008-06-09T14:01:40Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101166 |
| . |
| Reference:
|
[1] Hall W. S.: On the existence of periodic solutions for the equations $D\sb{tt}u+(-1)\sp{p}\,D\sb{x}\sp{2p}u=\varepsilon f(·,·,u)$.Jour. of Diff. Equations, 7, 509-526, 1970. MR 0265738 |
| Reference:
|
[2] Hall W. S.: Periodic solutions of a class of weakly nonlinear evolution equations.Arch. Rat. Mech. Anal., Vol. 39, 4, 294-322. Zbl 0211.12704, MR 0274914, 10.1007/BF00281367 |
| Reference:
|
[3] Lovicarová H.: Periodic solutions of a weakly nonlinear wave equation in one dimension.Czech. Math. J. 19, 1969, 324-342. MR 0247249 |
| Reference:
|
[4] Krylová N.: Periodic solutions of hyperbolic partial differential equation with quadratic dissipative term.Czech. Math. J. 20, 1970, 375-405. MR 0283358 |
| Reference:
|
[5] Krylová N., Vejvoda O.: A linear and weakly nonlinear equation of a beam: The boundary-value problem for free extremities and its periodic solutions.Czech. Math. J. 21, 1971, 535-566. MR 0289918 |
| Reference:
|
[6] Moser J.: A rapidly convergent iteration method and nonlinear partial differential equations.Ann. Scuola Norm. Super. Pisa, Ser. 3, 20, 1956, 265-315. MR 0199523 |
| Reference:
|
[7] Rabinowitz P. H.: Periodic solutions of nonlinear hyperbolic partial differential equations.Comm. Pure Appl. Math., 20, 1967, 145-205. Zbl 0152.10003, MR 0206507, 10.1002/cpa.3160200105 |
| Reference:
|
[8] Rabinowitz P. H.: Time periodic solutions of nonlinear wave equations.Manuscripta math., 5, 1971, 165-194. Zbl 0219.35062, MR 0326179, 10.1007/BF01325026 |
| Reference:
|
[9] De Simon L., Torelli C.: Soluzioni periodiche di equazioni a derivate parziali di tipo iperbolico non lineari.Rend. Sem. Mat. Univ. Padova XL, 1968, 380-401. Zbl 0198.13704, MR 0228836 |
| Reference:
|
[10] Torelli G.: Soluzioni periodiche dell'equazione non lineare $u\sb{tt}-u\sb{xx} + f(x, t, u) = 0$.Rend. Ist. di Matem. Univ. Trieste 1, 1969, 123-137. MR 0271520 |
| Reference:
|
[11] Petryshyn W. V.: On nonlinear $P$-compact operators in Banach space with applications to constructive fixed-point theorems.J. Math. Anal. Appl. 15, 1966, 228-242. Zbl 0149.10602, MR 0202014, 10.1016/0022-247X(66)90114-4 |
| Reference:
|
[12] Bers L., John F., Schechter W.: Partial Differential Equations.New York, Interscience 1964. Zbl 0126.00207 |
| Reference:
|
[13] Randol В.: A lattice-point problem II.TAMS 125, 1966, 101-113. Zbl 0161.04902, MR 0201408, 10.1090/S0002-9947-1966-0201408-4 |
| . |
