Conjugate points revisited and Neumann-Neumann problems

SIAM Review

Volumn 51, Issue 1, 2009, Pages 193-212

  Mannings, Robert S ^a  

^a HAVERFORD COLLEGE   (United States)

Author keywords

Calculus of variations; Conjugate points; Second variation

Indexed keywords

BASIC PROPERTIES; CALCULUS OF VARIATIONS; CONJUGATE POINTS; EIGEN VALUES; FINITE DIMENSIONS; HESSIAN MATRICES; NEUMANN BOUNDARY CONDITIONS; NEUMANN PROBLEMS; POINT APPROACHES; SECOND VARIATION; VARIATION OPERATORS;

CALCULATIONS; PROGRAMMING THEORY;

AEROSPACE VEHICLES;

EID: 59749101465     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/060668547     Document Type: Review

References (13)

1. S. S. ANTMAN, Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995.
2. G. BULMAN AND R. MANNING, Stability of an elastic rod buckling into a soft wall, Proc. R. Soc. London Ser. A, 461 (2005), pp. 2423-2450.
3. R. COURANT AND D. HILBERT, Methods of Mathematical Physics, Vol. I, Interscience, New York, 1953.
4. E. J. DOEDEL, H. B. KELLER, AND J. P. KERNÉVEZ, Numerical analysis and control of bifurcation problems, part I, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 1 (1991), pp. 493-520.
5. E. J. DOEDEL, H. B. KELLER, AND J. P. KERNÉVEZ, Numerical analysis and control of bifurcation problems, part II, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 1 (1991), pp. 745-772.
6. C. FOX, An Introduction to the Calculus of Variations, Oxford University Press, London, 1950.
7. I. M. GELFAND AND S. V. FOMIN, Calculus of Variations, Dover, Mineola, NY, 1963.
8. D. LAY, Linear Algebra and Its Applications, 3rd ed., Addison-Wesley, Boston, 2003.
9. R. MANNING, K. ROGERS, AND J. MADDOCKS, Isoperimetric conjugate points with application to the stability of DNA minicircles, Proc. R. Soc. London Ser. A, 454 (1998), pp. 3047-3074.
10. M. MORSE, Introduction to Analysis in the Large, Institute for Advanced Study, Princeton, NJ, 1951.
11. A. NAYLOR AND G. SELL, Linear Operator Theory in Engineering and Science, Springer-Verlag, New York, 1982.
12. H. SAGAN, Introduction to the Calculus of Variations, Dover, New York, 1969.
13. A. WEINSTEIN AND W. STENGER, Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications, Academic Press, New York, 1972.