A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations

Walter Craig

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1983)

  • Volume: 10, Issue: 1, page 125-167
  • ISSN: 0391-173X

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Craig, Walter. "A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 10.1 (1983): 125-167. <http://eudml.org/doc/83896>.

@article{Craig1983,
author = {Craig, Walter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {nonlinear dissipative hyperbolic equations; Nash-Moser implicit function theorems; Lyapunov-Schmidt decomposition},
language = {eng},
number = {1},
pages = {125-167},
publisher = {Scuola normale superiore},
title = {A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations},
url = {http://eudml.org/doc/83896},
volume = {10},
year = {1983},
}

TY - JOUR
AU - Craig, Walter
TI - A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1983
PB - Scuola normale superiore
VL - 10
IS - 1
SP - 125
EP - 167
LA - eng
KW - nonlinear dissipative hyperbolic equations; Nash-Moser implicit function theorems; Lyapunov-Schmidt decomposition
UR - http://eudml.org/doc/83896
ER -

References

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  1. [1] W. Craig, A bifurcation theory for periodic dissipative wave eqnations, Ph. D. Thesis, 1981, Courant Institute. 
  2. [2] M.G. Crandall - P.H. Rabinowitz, Bifurcation for simple eigenvalues. J. Functional Analysis, 8 (1971), pp. 321-340. Zbl0219.46015MR288640
  3. [3] M.G. Crandall - P.H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues, and linearized stability, Arch. Rational Mech. Anal., 52 (1973), pp. 161-180.. Zbl0275.47044MR341212
  4. [4] L. Hörmander, Implicit function theorems, Lectures at Stanford University, Summer 1977, preprint. 
  5. [5] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math., 33 (1980), pp. 43-101. Zbl0405.35056MR544044
  6. [6] J. Kohn - L. Nirenberg, Non-coercive boundary value problems, Comm. Pure-Appl. Math., 18 (1965), pp. 443-492. Zbl0125.33302MR181815
  7. [7] J. Kohn - L. Nirenberg, Degenerate elliptic-parabolic equations of second order,. Comm. Pure Appl. Math., 29 (1967), pp. 797-872. Zbl0153.14503MR234118
  8. [8] J. Moser, A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831. Zbl0104.30503MR132859
  9. [9] J. Moser, A rapidly convergent iteration method and won-linear partial differential equations I & II, Ann. Scuola Norm. Sup. Pisa, 20 (1966), pp. 265-315, 499-535. Zbl0144.18202
  10. [10] L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute Lecture Notes, 1974. Zbl0286.47037MR488102
  11. [11] P.H. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential' equations I, Comm. Pure Appl. Math., 20 (1967), pp. 145-205. Zbl0152.10003MR206507
  12. [12] P.H. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential' equations II, Comm. Pure Appl. Math., 22 (1969), pp. 15-39. Zbl0157.17301MR236504

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