Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity

Siegfried Carl

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 105-114
  • ISSN: 0137-6934

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Carl, Siegfried. "Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity." Banach Center Publications 29.1 (1994): 105-114. <http://eudml.org/doc/262720>.

@article{Carl1994,
author = {Carl, Siegfried},
journal = {Banach Center Publications},
keywords = {nonmonotone discontinuous nonlinearity; semilinear elliptic boundary value problem},
language = {eng},
number = {1},
pages = {105-114},
title = {Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity},
url = {http://eudml.org/doc/262720},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Carl, Siegfried
TI - Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 105
EP - 114
LA - eng
KW - nonmonotone discontinuous nonlinearity; semilinear elliptic boundary value problem
UR - http://eudml.org/doc/262720
ER -

References

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  1. [1] R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Vols. 1 and 2, Clarendon Press, Oxford 1975. Zbl0315.76051
  2. [2] V. Barbu and Th. Precupanu, Convexity and Optimization in Banach Spaces, Editura Academiei, Bucureşti, and Sijthoff, Noordhoff 1978. Zbl0379.49010
  3. [3] H. Brezis, Intégrales convexes dans les espaces de Sobolev, Israel J. Math. 13 (1972), 9-23. 
  4. [4] S. Carl, Ein konstruktiver Existenzsatz für Randwertprobleme elliptischer Differentialgleichungen zweiter Ordnung mit unstetiger Nichtlinearität, Math. Nachr. 138 (1988), 55-65. Zbl0666.35032
  5. [5] S. Carl and S. Heikkilä, An existence result for elliptic differential inclusions with discontinuous nonlinearity, Nonlinear Anal. 18 (1992), 471-479. Zbl0755.35039
  6. [6] S. Carl and S. Heikkilä, On extremal solutions of an elliptic boundary value problem involving discontinuous nonlinearities, Differential Integral Equations 5 (1992), 581-589. Zbl0785.35034
  7. [7] P. W. Davis and B. A. Fleishman, A discontinuous nonlinear problem: stability and convergence of iterations in a finite number of steps, Appl. Anal. 23 (1986), 139-157. Zbl0578.34010
  8. [8] J. Deuel and P. Hess, A criterion for the existence of solutions of nonlinear elliptic boundary value problems, Proc. Roy. Soc. Edinburgh 74A (1974/75), 49-54. Zbl0331.35028
  9. [9] J. I. Diaz and J. Hernandez, On the existence of a free boundary for a class of reaction-diffusion systems, SIAM J. Math. Anal. 15 (1984), 670-685. Zbl0556.35126
  10. [10] J. I. Diaz, Nonlinear Partial Differential Equations and Free Boundaries, Vol. 1: Elliptic Equations, Res. Notes in Math. 106, Pitman, Boston 1985. Zbl0595.35100
  11. [11] B. A. Fleishman, Convex superposition in piecewise-linear systems, J. Math. Anal. Appl. 6 (1963), 182-189. Zbl0116.06804
  12. [12] C. Großmann, Monotone discretization of two-point boundary value problems and related numerical methods, in: Discretization in Differential Equations and Enclosures, E. Adams, R. Ansorge, C. Großmann and H.-G. Roos (eds.), Akademie-Verlag, Berlin 1987, 99-122. 
  13. [13] S. Heikkilä, On an elliptic boundary value problem with discontinuous nonlinearity, Appl. Anal. 37 (1990), 183-189. Zbl0726.35045
  14. [14] E. Zeidler, Nonlinear Functional Analysis and its Applications III: Variational Methods, Springer, New York 1985. Zbl0583.47051

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