Global continuation in nonlinear elasticity

Archive for Rational Mechanics and Analysis

Volumn 143, Issue 1, 1998, Pages 1-28

  Healey, Timothy J ^a   Simpson, Henry C ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032376336     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050098     Document Type: Article

References (51)

1. R. A. ADAMS, Sobolev Spaces, Academic Press, New York, 1975.
2. S. AGMON, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962) 119-147.
3. S. AGMON, A. DOUGLIS & L. NIRENBERG, Esimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math. 17 (1964) 35-92.
4. J. C. ALEXANDER & S. S. ANTMAN, Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems, Arch. Rational Mech. Anal. 76 (1981) 339-354.
5. J. C. ALEXANDER & J. A. YORKE, The implicit function theorem and global methods of cohomology, J. Funct. Anal. 21 (1976) 330-339.
6. S. S. ANTMAN, Continuation methods in nonlinear elasticity, Proceedings 1st World Congress of Nonlinear Analysis, 1992, Ed. V. LAKSHMIKANTHAM, De Gruyter, 1996, 827-838
7. S. S. ANTMAN & M. LANZA DE CHISTOFORIS, The large deformation of nonlinearly elastic tubes in two-dimensional flows, SIAM J. Math. Anal. 22 (1991) 1193-1221.
8. J. M. BALL, Convexity conditions and existence theorems in nonlinear elasticity theory, Arch. Rational Mech. Anal. (1977) 337-403
9. M. A. BIOT, Mechanics of Incremental Deformations, John Wiley & Sons, New York, 1965.
10. F. E. BROWDER, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Symp. Pure Math. 18, Part 2 (1976).
11. P. G. CIARLET, Mathematical Elasticity, Vol. I, North-Holland, Amsterdam, 1988.
12. P. G. CIARLET & J. NEČAS, Injectivity and self-contact in nonlinear elasticity, Arch. Rational Mech. Anal. (1987) 171-188.
13. D. G. DE FIGUEIREDO, The coerciveness problem for forms over vector valued functions, Comm. Pure Appl. Math. 16 (1963) 63-94.
14. K. D. ELWORTHY & A. J. TROMBA, Degree theory on Banach manifolds, Proc. Symp. Pure Math. 18, Part 1, Amer. Math. Soc. (1970) 86-94.
15. J. ERICKSEN, Special topics in nonlinear elastostatics, in Advances in Applied Mechanics 17, Ed. C.-S. YIH, Academic Press, New York, 1977.
16. C. C. FENSKE, Analytische Theorie des Abbildungsgrades in Banachräumen, Math. Nachr. 48 (1971) 279-290.
17. C. C. FENSKE, Extensio gradus ad quasdam applicationes Fredholmii, Mitt. Math. Seminar, Giessen 121 (1976) 65-70.
18. P. FITZPATRICK & J. PEJSACHOWICZ, Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems, Mem. Amer. Math. Soc. 101, No. 483 (1993).
19. P. FITZPATRICK & J. PEJSACHOWICZ, Parity and generalized multiplicity, Trans. Amer. Math. Soc. 326 (1991) 281-305.
20. 2 Fredholm mappings I, J. Reine Angew. Math. 427 (1992) 1-33.
21. P. FITZPATRICK, J. PEJSACHOWICZ & P. J. RABIER, Orientability of Fredholm families and topological degree for orientable nonlinear Fredholm mappings, 3. Funct. Anal. 124 (1994) 1-39.
22. A. FRIEDMAN, Partial Differential Equations, Holt, Rinehart, Winston, New York, 1969.
23. I. C. GOHBERG & M. G. KREIN, The basic propositions on defect numbers, root numbers, and indices of linear operators, Uspehi Mat. Nauk. 12(74) (1957) 43-118; English Transl., Amer. Math. Soc. Transl. (Series 2) 13 (1960) 185-265.
24. I. C. GOHBERG & M. G. KREIN, The basic propositions on defect numbers, root numbers, and indices of linear operators, Uspehi Mat. Nauk. 12(74) (1957) 43-118; English Transl., Amer. Math. Soc. Transl. (Series 2) 13 (1960) 185-265.
25. V. GUILLEMIN & A. POLLACK, Differential Topology, Prentice Hall, Englewood Cliffs, N.J., 1974.
26. N. M. GÜNTER, Potential Theory and its Application to Basic Problems of Mathematical Physics, Frederick Ungar, New York, 1967.
27. T. J. HEALEY & H. KIELHÖFER, Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations, Arch. Rational Mech. Anal. 113 (1991) 299-311.
28. T. J. HEALEY & H. KIELHÖFER, Symmetry and preservation of nodal structure in elliptic equations satisfying fully nonlinear Neumann boundary conditions, m Bifurcation and Symmetry, Eds. E. L. ALLGOWER, K. BOEHMER & M. GOLUBITSKY, Birkhäuser, Basel, 1992.
29. T. J. HEALEY & P. ROSAKIS, Unbounded branches of classical infective solutions in the forced displacement problem of nonlinear elastostatics, J. Elasticity 49 (1997) 65-78.
30. T. KATO, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1976.
31. H. KIELHÖFER, Multiple eigenvalue bifurcation for Fredholm mappings, J. Reine Angew. Math. 358 (1985) 104-124.
32. H. KIELHÖFER, Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme, Math. Z. 142 (1975) 131-160
33. R. J. KNOPS & L. E. PAYNE, Uniqueness Theorems in Linear Elasticity, Springer-Verlag, New York, 1971.
34. M. A. KRASNOSEL'SKII, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, New York, 1964.
35. S. LANG, Real Analysis, 2nd Ed., Addison-Wesley, Reading, Mass., 1983.
36. H. LE DRET, Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence, J. Elast. 17 (1987) 123-141.
37. N. G. LLOYD, Degree Theory, Cambridge University Press, London, 1978.
38. J. LERAY & J. SCHAUDER, Topologie et équations fonctionnelles, Ann. Sci. Ec. Norm. Sup. (3) 51 (1934) 45-78.
39. J. E. MARSDEN & T. J. R. HUGHES, Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New Jersey, 1983.
40. J. C. PAUMIER, Existence theorems for nonlinear elastic plates with periodic boundary conditions, J. Elast. 23 (1990) 233-252.
41. J. PEETRE, Another approach to elliptic boundary problems, Comm. Pure Appl. Math. 14 (1961) 711-731
42. F. QUINN & A. SARD, Hausdorffconullity of critical images of Fredholm maps, Amer. J. Math. 94 (1972) 1101-1110.
43. P. H. RABINOWITZ, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971) 487-513.
44. H. C. SIMPSON & S. J. SPECTOR, On the positivity of the second variation in finite elasticity, Arch. Rational Mech. Anal. 98 (1987) 1-30.
45. H. C. SIMPSON & S. J. SPECTOR, Necessary conditions at the boundary for minimizers infinite elasticity, Arch. Rational Mech. Anal. 107 (1989) 105-125.
46. S. SMALE, An infinite dimensional version of Sard's theorem. Amer. J. Math. 87 (1965) 861-866.
47. A. TAYLOR, Introduction to Functional Analysis, Wiley, New York, 1958.
48. T. VALENT, Boundary Value Problems of Finite Elasticity, Springer-Verlag, New York, 1988.
49. W. VON WAHL, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen, II. math.-phys. K1 11 (1972) 231-258.
50. G. T. WHYBURN, Topological Analysis, Princeton University Press, Princeton, New Jersey, 1964.
51. E. ZEIDLER, Nonlinear Functional Analysis and its Applications, I, Springer-Verlag, New York, 1986.