The construction of principal spectral curves for Lane-Emden systems and applications

Marcos Montenegro

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 1, page 193-229
  • ISSN: 0391-173X

How to cite

top

Montenegro, Marcos. "The construction of principal spectral curves for Lane-Emden systems and applications." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.1 (2000): 193-229. <http://eudml.org/doc/84401>.

@article{Montenegro2000,
author = {Montenegro, Marcos},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Lane-Emden system; spectral theory},
language = {eng},
number = {1},
pages = {193-229},
publisher = {Scuola normale superiore},
title = {The construction of principal spectral curves for Lane-Emden systems and applications},
url = {http://eudml.org/doc/84401},
volume = {29},
year = {2000},
}

TY - JOUR
AU - Montenegro, Marcos
TI - The construction of principal spectral curves for Lane-Emden systems and applications
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 1
SP - 193
EP - 229
LA - eng
KW - Lane-Emden system; spectral theory
UR - http://eudml.org/doc/84401
ER -

References

top
  1. [1] A. Alvino - V. Ferone - G. Trombetti, On the properties of some nonlinear eigenvalues, SIAM J. Math. Anal., vol. 29, n. 2 (1998), 437-451. Zbl0908.35094MR1616519
  2. [2] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev.18 (1976), 620-709. Zbl0345.47044MR415432
  3. [3] A. Anane, Simplicité et isolation de la première valeur propre du p-laplacien avec poids, C. R. Acad. Sci. Paris305 (1987), 725-728. Zbl0633.35061
  4. [4] H. Berestycki - L. Nirenberg - S.R.S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math.XLVII (1994), 47-92. Zbl0806.35129
  5. [5] I. Birindelli, Hopf's lemma and anti-maximum principle in general domains, J. Differential Equations119 (1995), 450-472. Zbl0831.35114
  6. [6] I. Birindelli - E. Mitidieri - G. Sweers, Existence of the principal eigenvalue for cooperative elliptic systems in a general domain, preprint. Zbl0940.35147
  7. [7] J.M. Bony, Principe du maximum dans les espaces de Sobolev, C. R. Acad. Sci. Paris Série A265 (1967), 333-336. Zbl0164.16803
  8. [8] H. Brézis - S. Kamin, Sublinear elliptic equations in R N, Manuscripta Math.74 (1992), 87-106. Zbl0761.35027
  9. [9] K.J. Brown - C.C. Lin, On the existence of positive eigenfunctions for a eigenvalue problem with indefinite weight-function, J. Math. Anal. Appl.75 (1980), 112-120. Zbl0437.35058
  10. [10] R.S. Cantrell - K. Schmidt, On the eigenvalue problem for coupled elliptic systems, SIAM J. Math. Anal.17 (1986), 850-862. Zbl0606.35033
  11. [11] PH. Clément - D.G. De Figueiredo - E. Mitidieri, Positive solutions of semilinear elliptic systems, Comm. Partial Differential Equations, vol. 17, n. 5 & 6 (1992), 923-940. Zbl0818.35027
  12. [12] PH. Clément - R.C.A.M. Van Der Vorst, On a semilinear elliptic system, Differential Integral Equations8 (1995), 1317-1329. Zbl0835.35041MR1329843
  13. [13] D.G. De Figueiredo - P.L. Felmer, On superquadratic elliptic systems, Trans. Amer. Math. Soc.343 (1994), 99-116. Zbl0799.35063MR1214781
  14. [14] B. De Pagter, Irreducible compact operators, Math. Z.192 (1986), 149-153. Zbl0607.47033MR835399
  15. [15] M.D. Donsker - S.R.S. Varadhan, On a variational formula for the principal eigenvalue for operators with maximum principle, Proc. Nat. Acad. Sci. U.S.A.72 (1975), 780-783. Zbl0353.49039MR361998
  16. [16] M.D. Donsker - S.R.S. Varadhan, On the principal eigenvalue of second order elliptic differential operators, Comm. Pure Appl. Math.29 (1976), 595-621. Zbl0356.35065MR425380
  17. [17] P.L. Felmer - S. Martínez, existence and uniqueness of positive solutions to certain differential systems, Adv. Differential Equations, vol. 3, n. 4 (1998), 575-593. Zbl0946.35028MR1659242
  18. [18] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer-Verlag, 1983. Zbl0562.35001MR737190
  19. [19] J.-P. Gossez - E. Lami-Dozo, On the principal eigenvalue of a second order linear elliptic problem, Arch. Rational Mech. Anal.89 (1985), 169-175. Zbl0585.35075MR786544
  20. [20] P. Hess, On the eigenvalue problem for weakly coupled elliptic systems, Arch. Rational Mech. Anal.81 (1983), 151-159. Zbl0509.35029MR682266
  21. [21] P. Hess - T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations5 (1980), 999-1030. Zbl0477.35075MR588690
  22. [22] J. Hulshof - R.C.A.M. Van Der Vorst, Differential systems with strongly indefinite variational structure, J. Funct. Anal.114 (1993), 32-58. Zbl0793.35038MR1220982
  23. [23] M.A. Krasnoselskii, Fixed points of cone-compressing or cone-extending operators, Sov. Math. Dokl.1 (1960), 1285-1288. Zbl0098.30902MR131158
  24. [24] M.A. Krasnoselskii, "Positive Solutions of Operator Equations", Noordhoff, 1964. Zbl0121.10604MR181881
  25. [25] M.G. Krein - M.A. Rutman, Linear operators leaving invariant a cone in a Banach space, Amer. Math. Soc. Transl.10 (1962), 199-325. MR38008
  26. [26] J. López-Gómez, The maximum principle and the existence of principal eigenvalue for some linear weighted boundary value problems, J. Differential Equations127 (1996), 263-294. Zbl0853.35078MR1387266
  27. [27] J. López-Gómez - M. Molina-Meyer, The maximum principle for cooperative weakly coupled elliptic systems and some applications, Differential Integral Equations, vol. 7, n. 2 (1994), 383-398. Zbl0827.35019MR1255895
  28. [28] A. Manes - A.M. Micheletti, Un'estensione della teoria variazionale classica degli autovalori per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital.7 (1973), 285-301. Zbl0275.49042MR344663
  29. [29] M. Montenegro, Sublinearity for semilinear elliptic systems, preprint. 
  30. [30] M. Montenegro, Liouville type theorems and blow-up for semilinear differential systems, preprint. 
  31. [31] M. Montenegro, Existence of solutions for some semilinear elliptic systems with singular coefficients, to appear in Nonlinear Analysis. Zbl1027.35030MR1835614
  32. [32] R.D. Nussbaum - Y. Pinchover, On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications, J. Anal. Math.59 (1992), 161-177. Zbl0816.35095MR1226957
  33. [33] M.H. Protter, The generalized spectrum of second orderelliptic systems, Rocky Mountain J. Math.9 (1979), 503-518. Zbl0422.35061MR528748
  34. [34] M.H. Protter - H.F. Weinberger, "Maximum Principles in Differential Equations", Prentice Hall, New Jersey, 1967. Zbl0153.13602MR219861
  35. [35] G. Sweers, Strong positivity in C(Ω) for elliptic systems, Math. Z.209 (1992), 251-271. Zbl0727.35045
  36. [36] R.C.A.M. Van Der Vorst, Variational identities and applications to differential systems, Arch. Rational Mech. Anal.116 (1991), 375-398. Zbl0796.35059MR1132768
  37. [37] W. Walter, Sturm-Liouville theory for the radial Δp-operator, Math. Z.227, (1998) 175-185. Zbl0915.34022

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.