Hard implicit function theorem and small periodic solutions to partial differential equations

Pavel Krejčí

Commentationes Mathematicae Universitatis Carolinae (1984)

  • Volume: 025, Issue: 3, page 519-536
  • ISSN: 0010-2628

How to cite

top

Krejčí, Pavel. "Hard implicit function theorem and small periodic solutions to partial differential equations." Commentationes Mathematicae Universitatis Carolinae 025.3 (1984): 519-536. <http://eudml.org/doc/17340>.

@article{Krejčí1984,
author = {Krejčí, Pavel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Existence; small solutions; abstract equation; Banach spaces; a priori estimates; Nash's iteration procedure; classical priodic solutions; Dirichlet boundary conditions},
language = {eng},
number = {3},
pages = {519-536},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hard implicit function theorem and small periodic solutions to partial differential equations},
url = {http://eudml.org/doc/17340},
volume = {025},
year = {1984},
}

TY - JOUR
AU - Krejčí, Pavel
TI - Hard implicit function theorem and small periodic solutions to partial differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1984
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 025
IS - 3
SP - 519
EP - 536
LA - eng
KW - Existence; small solutions; abstract equation; Banach spaces; a priori estimates; Nash's iteration procedure; classical priodic solutions; Dirichlet boundary conditions
UR - http://eudml.org/doc/17340
ER -

References

top
  1. M. ALTMAN, A series of papers on nonlinear evolution equations, Nonlin. Anal., Theory, Meth., Appl. 8 (1984), No. 5, pp. 457 - 499. (1984) MR0741601
  2. W. CRAIG, A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations, Ann. Scuola Norm. Sup. Pisa, ser. IV, vol. X (1983), pp. 125 - 168. (1983) Zbl0518.35057MR0713113
  3. B. D. CRAVEN M. Z. NASHED, Generalized implicit function theorems when the derivative has no bounded inverse, Nonlin. Anal., Theory, Meth., Appl. 6 (1982), pp. 375-387. (1982) MR0654813
  4. M. R. HESTENES, Extension of the range of a differentiable function, Duke Math. J. 8 (1941), pp. 183 - 192. (1941) Zbl0024.38602MR0003434
  5. L. HÖRMANDER, The boundary problems of physical geodesy, Arch. Rat. Keen. Anal. 62 (1976), pp. 1 - 52. (1976) MR0602181
  6. S. KLAINERMAN, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), pp. 43 - 101. (1980) Zbl0405.35056MR0544044
  7. P. KREJČÍ, Periodic vibrations of the electromagnetic field in ferromagnetic media, (in Czech). Candidate thesis, Mathematical Institute of the Czechoslovak Academy of Sciences, Prague, 1984. (1984) 
  8. J. MOSER, A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sci. 47 (1961), pp. 1824 - 1831. (1961) Zbl0104.30503MR0132859
  9. J. MOSER, A rapidly-convergent iteration method and nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265 - 315, 499 - 535. (1966) 
  10. J. NASH, The embedding problem for Riemannian manifolds, Ann. of Math. 63 (1956), pp. 20 - 63. (1956) MR0075639
  11. L. NIRENBERG, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), pp. 115 - 162. (1959) Zbl0088.07601MR0109940
  12. H. PETZELTOVÁ, Application of Moser's method to a certain type of evolution equations, Czech. Math. J. 33 (1983), pp. 427 - 434. (1983) Zbl0547.35081MR0718925
  13. V. PTÁK, A modification of Newton's method, Čas. Pěst. Mat. 101 (1976), pp. 188 - 194. (1976) Zbl0328.46013MR0443326
  14. P. H. RABINOWITZ, Periodic solutions of nonlinear hyperbolic partial differential equations II, Comm. Pure Appl. Math. 22 (1969), pp. 15 - 39. (1969) Zbl0157.17301MR0236504
  15. J. T. SCHWARTZ, On Nash's implicit functional theorem, Comm. Pure Appl. Math. 13 (1960), pp. 509 - 530. (1960) Zbl0178.51002MR0114144
  16. J. SHATAH, Global existence of small solutions to nonlinear evolution equations, J. Diff. Eq. 46 (1982), pp.409 - 425. (1982) Zbl0518.35046MR0681231
  17. Y. SHIBATA, On the global existence of classical solutions of mixed problem for some second order non-linear hyperbolic operators with dissipative term in the interior domain, Funkc. Ekv. 25 (1982), pp. 303 - 345. (1982) MR0707564
  18. Y. SHIBATA, On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first-order dissipation in the exterior domain, Tsukuba J. Math. 7 (1983), pp. 1 - 68. (1983) Zbl0524.35071MR0703667

Citations in EuDML Documents

top
  1. Eduard Feireisl, Small time-periodic solutions to a nonlinear equation of a vibrating string
  2. Eduard Feireisl, Bounded, almost-periodic, and periodic solutions to fully nonlinear telegraph equations
  3. Eduard Feireisl, Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
  4. Milan Stedry, Small time periodic solutions of fully nonlinear telegraph equations in more spatial dimensions
  5. Pavel Krejčí, Periodic solutions to Maxwell equations in nonlinear media
  6. Eduard Feireisl, Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations
  7. Eduard Feireisl, Global in time solutions to quasilinear telegraph equations involving operators with time delay

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.