Pacific Journal of Mathematics

Applications of topological transversality to differential equations. I. Some nonlinear diffusion problems.

A. Granas, R. B. Guenther, and J. W. Lee

Article information

Source
Pacific J. Math. Volume 89, Number 1 (1980), 53-67.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102779368

Zentralblatt MATH identifier
0453.34018

Mathematical Reviews number (MathSciNet)
MR596916

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 35G15: Boundary value problems for linear higher-order equations 57R99: None of the above, but in this section

Citation

Granas, A.; Guenther, R. B.; Lee, J. W. Applications of topological transversality to differential equations. I. Some nonlinear diffusion problems. Pacific Journal of Mathematics 89 (1980), no. 1, 53--67. http://projecteuclid.org/euclid.pjm/1102779368.


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References

  • [1] W. H. Bossert and J. M. Diamond, Standing-gradient osmotic flow, J. General Phy- siology, 50 (1967), 2061-2083.
  • [2] J. Dugundji and A. Granas, Fixed Point Theory I, Monografic Matematyczne, Warsaw, to appear.
  • [3] A. Granas, Sur la methode de continuity de Poincare, Comptes Rendus Acad. Sci. Paris, 282 (1976), 983-985-
  • [4] A. Granas, R. B. Guenther and J. W. Lee, On a theorem of S. Bernstein, Pacific J. Math., 74 (1978), 67-82.
  • [5] A. Granas,The shooting method for the numerical solution of a class of nonlinear boundary value problems, SIAM J. Numer. Analysis, 16 (1979), 828-836. . R. G. Kellogg, Uniqueness in the Schauder fixed point theorem, Proc. AMS, GO(1976), 207-210.
  • [7] A. Granas,Osmotic flow in a tube with stagnant points, Technical Note BN-818, IFDAM, Univ. of Maryland, College Park, MD, 1975.

See also

  • II : A. Granas, R. B. Guenther, J. W. Lee. Topological transversality. II. Applications to the Neumann problem for $y^{\prime\prime}=f(t,\,y,\,y^{\prime})$. Pacific Journal of Mathematics volume 104, issue 1, (1983), pp. 95-109.