Geometry of some simple nonlinear differential operators

H. P. Mc Kean; J. C. Scovel

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 2, page 299-346
  • ISSN: 0391-173X

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Mc Kean, H. P., and Scovel, J. C.. "Geometry of some simple nonlinear differential operators." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.2 (1986): 299-346. <http://eudml.org/doc/83982>.

@article{McKean1986,
author = {Mc Kean, H. P., Scovel, J. C.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {nonlinear differential operator; local folds; cusps; higher singularities; degree of the singularity; Dirichlet boundary conditions; convex surface; principal direction of negative curvature relative},
language = {eng},
number = {2},
pages = {299-346},
publisher = {Scuola normale superiore},
title = {Geometry of some simple nonlinear differential operators},
url = {http://eudml.org/doc/83982},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Mc Kean, H. P.
AU - Scovel, J. C.
TI - Geometry of some simple nonlinear differential operators
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 2
SP - 299
EP - 346
LA - eng
KW - nonlinear differential operator; local folds; cusps; higher singularities; degree of the singularity; Dirichlet boundary conditions; convex surface; principal direction of negative curvature relative
UR - http://eudml.org/doc/83982
ER -

References

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  1. [1] A. Ambrosetti - G. Prodi, On the inversion of some differentiable maps between Banach spaces with singularities, Ann. Mat., 93 (1972), 231-246. Zbl0288.35020MR320844
  2. [2] M.S. Berger, Non-linearity and Functional Analysis, Academic Press, N.Y.C., 1977. 
  3. [3] M.S. Berger - P.T. Church, Complete, integrability and perturbation of a nonlinear Dirichlet problem (I), Indiana Univ. Math. J., 28 (1979) 935-952. Zbl0425.35090MR551157
  4. [4] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience Publishers, New York, 1953. Zbl0051.28802MR65391
  5. [5] M. Golubitski - V. Guillemin, Stable Mappings and their Singularities, Springer-Verlag, N.Y.C., 1973. Zbl0294.58004MR341518
  6. [6] A.C. Lazer - P.J. McKenna, On a conjecture related to the number of solutions of a nonlinear Dirichlet problem, Proc. Roy. Soc. Edinburgh, to appear. Zbl0533.35037
  7. [7] H.P. McKean, Curvature of an ∞-dimensional manifold related to Hill's equation, J. Differential Geom., 17 (1982), 523-529. Zbl0481.58013
  8. [8] J.C. Scovel, Geometry of some nonliner differential operators, Ph.D. Thesis, New York University, 1983. 
  9. [9] J.C. Scovel, Geometry of some simple nonlinear differential operators, part II, sub. to J.D.E. Mar 1985 
  10. [10] H. Whitney, On singularities of mappings, Ann. of Math. (1955), 374-416. Zbl0068.37101MR73980

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