On Impasse Points of Quasilinear Differential-Algebraic Equations

Journal of Mathematical Analysis and Applications

Volumn 181, Issue 2, 1994, Pages 429-454

  Rabier, Patrick J ^a   Rheinboldt, Werner C ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000474711     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1006/jmaa.1994.1033     Document Type: Article

References (13)

1. R. Abraham, J. E. Marsden, and T. Ratiu, “Manifolds, Tensor Analysis and Applications,” 2nd ed. Springer-Verlag, New York, 1988.
2. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, “Singularities of Differentiable Maps," Vol. I, translation from the Russian, Birkhauser, Boston, MA, 1985.
3. L. O. Chua, “Introduction to Nonlinear Networks," McGraw-Hill, New York, 1969.
4. L. O. Chua and A. C. Deng, Impasse points, I, Numerical aspects, Internal. J. Circuit Theory Appl. 17 (1989), 213-235.
5. Dieudonne D., “Elements d’Analyse,” Vol. 3, Gauthier-Villars, Paris, 1970.
6. M. Golubitsky and V. Guillemin, “Stable Mappings and Their Singularities," Graduate Texts in Mathematics, Vol. 14, Springer-Verlag, New York, 1973.
7. R. Maerz, On quasilinear index 2 differntial-algebraic equations, in “Seminar Notes, Berlin Seminar on Differential-Algebraic Equations, 1991," pp. 39-60.
8. P. J. Rabier, Implicit differential equations near a singular point, J. Math. Anal. Appl. 144 (1989), 425-449.
9. P. J. Rabier and W. C. Rheinboldt, A general existence and uniqueness theory for implicit differential-algebraic equations, J. Differential Integral Equations 4 (1991), 563-582.
10. P. J. Rabier and W. C. Rheinboldt, A geometric treatment of implicit differential-algebraic equations, J. Differential Equations, in press.
11. P. J. Rabier and W. C. Rheinboldt, On the computation of impasse points of quasilinear differential-algebraic equations, Math. Comp., to appear.
12. S. Smale, On the mathematical foundation of electrical networks, J. Differential Geometry 7 (1972), 193-210.
13. F. Takens, “Constrained Equations; A Study of Implicit Differential Equations and Their Discontinuous Solutions," Lecture Notes in Math. Vol. 525, pp. 143-234, Springer-Verlag, New York, 1976.