A minimization problem associated with elliptic systems of Fitz–Hugh–Nagumo type

E. N. Dancer; Shusen Yan

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 2, page 237-253
  • ISSN: 0294-1449

How to cite

top

Dancer, E. N., and Yan, Shusen. "A minimization problem associated with elliptic systems of Fitz–Hugh–Nagumo type." Annales de l'I.H.P. Analyse non linéaire 21.2 (2004): 237-253. <http://eudml.org/doc/78617>.

@article{Dancer2004,
author = {Dancer, E. N., Yan, Shusen},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Elliptic systems; Multiple layer},
language = {eng},
number = {2},
pages = {237-253},
publisher = {Elsevier},
title = {A minimization problem associated with elliptic systems of Fitz–Hugh–Nagumo type},
url = {http://eudml.org/doc/78617},
volume = {21},
year = {2004},
}

TY - JOUR
AU - Dancer, E. N.
AU - Yan, Shusen
TI - A minimization problem associated with elliptic systems of Fitz–Hugh–Nagumo type
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 2
SP - 237
EP - 253
LA - eng
KW - Elliptic systems; Multiple layer
UR - http://eudml.org/doc/78617
ER -

References

top
  1. [1] Alberti G., Ambrosio L., Cabré X., On a long-standing conjecture of E. De Giorgi: symmetry in 3d for general nonlinearities and a local minimality property, Acta Appl. Math.65 (2001) 9-33. Zbl1121.35312MR1843784
  2. [2] Ambrosio L., Cabré X., Entire solutions of semilinear elliptic equations in R3 and a conjecture of de Giorgi, J. Amer. Math. Soc.13 (2000) 725-739. Zbl0968.35041MR1775735
  3. [3] Berestycki H., Caffarelli L., Nirenberg L., Further qualitative properties for elliptic equations in unbounded domains, Ann Scuola Norm. Sup. Pisa C1. Sci.25 (1997) 69-94. Zbl1079.35513MR1655510
  4. [4] Brezis H., Opŕateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert, North-Holland, Amsterdam, 1973. Zbl0252.47055MR348562
  5. [5] Chafee N., A stability analysis for a semilinear parabolic partial differential equation, J. Differential Equations15 (1974) 522-540. Zbl0271.35043MR358042
  6. [6] Clément P., Peletier L.A., On a nonlinear eigenvalue problem occurring in population genetics, Proc. Royal Soc. Edinburgh Sect. A100 (1985) 85-101. Zbl0569.34021MR801846
  7. [7] Clément P., Sweers G., Existence and multiplicity results for a semilinear eigenvalue problem, Ann. Scuola Norm. Sup. Pisa14 (1987) 97-121. Zbl0662.35045MR937538
  8. [8] Dancer E.N., On the number of positive solutions of weakly non-linear elliptic equations when a parameter is large, Proc. London Math. Soc.53 (1986) 429-452. Zbl0572.35040MR868453
  9. [9] De Giorgi E., Convergence problems for functionals and operators, in: Proc. Int. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978, pp. 131-188. Zbl0405.49001MR533166
  10. [10] deFigueiredo D.G., Mitidieri E., A maximum principle for an elliptic system and applications to semilinear problems, SIAM J. Math. Anal.17 (1986) 836-849. Zbl0608.35022MR846392
  11. [11] Ghoussoub N., Gui C., On a conjecture of De Giorgi and some related problem, Math. Ann.311 (1998) 481-491. Zbl0918.35046MR1637919
  12. [12] Ghoussoub N., Gui C., On De Giorgi's conjecture in dimensions 4 and 5, Ann. Math.157 (2003) 313-334. Zbl1165.35367MR1954269
  13. [13] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
  14. [14] Klaasen G.A., Mitidieri E., Standing wave solutions for a system derived from the FitzHugh–Nagumo equation for nerve conduction, SIAM J. Math. Anal.17 (1986) 74-83. Zbl0593.35043MR819214
  15. [15] Klaasen G.A., Troy W.C., Stationary wave solutions of a system of reaction–diffusion equations derived from the FitzHugh–Nagumo equations, SIAM J. Appl. Math.44 (1984) 96-110. Zbl0543.35051MR730003
  16. [16] Lazer A.C., Mckenna P.J., On steady state solutions of a system of reaction–diffusion equations from biology, Nonlinear Anal.6 (1982) 523-530. Zbl0488.35039MR664014
  17. [17] Modica L., Gradient theory of phase transitions and minimal interface criteria, Arch. Rational Mech. Anal.98 (1987) 123-142. Zbl0616.76004MR866718
  18. [18] Reinecke C., Sweers G., A boundary layer solution to a semilinear elliptic system of FitzHugh–Nagumo type, C. R. Acad. Sci. Paris Sér. I. Math.329 (1999) 27-32. Zbl0931.35046MR1703287
  19. [19] Reinecke C., Sweers G., A positive solution on RN to s system of elliptic equations of FitzHugh–Nagumo type, J. Differential Equations153 (1999) 292-312. Zbl0929.35042MR1683624
  20. [20] Reinecke C., Sweers G., Existence and uniqueness of solutions on bounded domains to a FitzHugh–Nagumo type elliptic system, Pacific J. Math.197 (2001) 183-211. Zbl1066.35069MR1810215
  21. [21] Reinecke C., Sweers G., Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type, Math. Nachr.251 (2003) 64-87. Zbl1118.35009MR1960805
  22. [22] Sternberg P., The effect of a singular perturbation on nonconvex variational problem, Arch. Rational Mech. Anal.101 (1988) 202-260. Zbl0647.49021MR930124

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.