Periodic solutions of the equation u t t + u x x x x = ε f ( · , · , u , u t )

Hana Petzeltová

Czechoslovak Mathematical Journal (1973)

  • Volume: 23, Issue: 2, page 269-285
  • ISSN: 0011-4642

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Petzeltová, Hana. "Periodic solutions of the equation $u_{tt}+u_{xxxx}=\varepsilon f(\cdot ,\cdot ,u,u_t)$." Czechoslovak Mathematical Journal 23.2 (1973): 269-285. <http://eudml.org/doc/12721>.

@article{Petzeltová1973,
author = {Petzeltová, Hana},
journal = {Czechoslovak Mathematical Journal},
language = {eng},
number = {2},
pages = {269-285},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic solutions of the equation $u_\{tt\}+u_\{xxxx\}=\varepsilon f(\cdot ,\cdot ,u,u_t)$},
url = {http://eudml.org/doc/12721},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Petzeltová, Hana
TI - Periodic solutions of the equation $u_{tt}+u_{xxxx}=\varepsilon f(\cdot ,\cdot ,u,u_t)$
JO - Czechoslovak Mathematical Journal
PY - 1973
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 2
SP - 269
EP - 285
LA - eng
UR - http://eudml.org/doc/12721
ER -

References

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  1. 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 ( · , · , u ) , Jour. of Diff. Equations, 7, 509-526, 1970. (1970) MR0265738
  2. Hall W. S., 10.1007/BF00281367, Arch. Rat. Mech. Anal., Vol. 39, 4, 294-322. Zbl0211.12704MR0274914DOI10.1007/BF00281367
  3. Lovicarová H., Periodic solutions of a weakly nonlinear wave equation in one dimension, Czech. Math. J. 19, 1969, 324-342. (1969) MR0247249
  4. Krylová N., Periodic solutions of hyperbolic partial differential equation with quadratic dissipative term, Czech. Math. J. 20, 1970, 375-405. (1970) MR0283358
  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. (1971) MR0289918
  6. Moser J., A rapidly convergent iteration method and nonlinear partial differential equations, Ann. Scuola Norm. Super. Pisa, Ser. 3, 20, 1956, 265-315. (1956) MR0199523
  7. Rabinowitz P. H., 10.1002/cpa.3160200105, Comm. Pure Appl. Math., 20, 1967, 145-205. (1967) Zbl0152.10003MR0206507DOI10.1002/cpa.3160200105
  8. Rabinowitz P. H., 10.1007/BF01325026, Manuscripta math., 5, 1971, 165-194. (1971) Zbl0219.35062MR0326179DOI10.1007/BF01325026
  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. (1968) Zbl0198.13704MR0228836
  10. Torelli G., Soluzioni periodiche dell’equazione non lineare u t t - u x x + f ( x , t , u ) = 0 , Rend. Ist. di Matem. Univ. Trieste 1, 1969, 123-137. (1969) MR0271520
  11. Petryshyn W. V., 10.1016/0022-247X(66)90114-4, J. Math. Anal. Appl. 15, 1966, 228-242. (1966) Zbl0149.10602MR0202014DOI10.1016/0022-247X(66)90114-4
  12. Bers L., John F., Schechter W., Partial Differential Equations, New York, Interscience 1964. (1964) Zbl0126.00207
  13. Randol В., 10.1090/S0002-9947-1966-0201408-4, TAMS 125, 1966, 101-113. (1966) Zbl0161.04902MR0201408DOI10.1090/S0002-9947-1966-0201408-4

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