# Geometry of some simple nonlinear differential operators

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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topMc 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

top- [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] M.S. Berger, Non-linearity and Functional Analysis, Academic Press, N.Y.C., 1977.
- [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] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience Publishers, New York, 1953. Zbl0051.28802MR65391
- [5] M. Golubitski - V. Guillemin, Stable Mappings and their Singularities, Springer-Verlag, N.Y.C., 1973. Zbl0294.58004MR341518
- [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] H.P. McKean, Curvature of an ∞-dimensional manifold related to Hill's equation, J. Differential Geom., 17 (1982), 523-529. Zbl0481.58013
- [8] J.C. Scovel, Geometry of some nonliner differential operators, Ph.D. Thesis, New York University, 1983.
- [9] J.C. Scovel, Geometry of some simple nonlinear differential operators, part II, sub. to J.D.E. Mar 1985
- [10] H. Whitney, On singularities of mappings, Ann. of Math. (1955), 374-416. Zbl0068.37101MR73980

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