Existence results for quasilinear problems via ordered sub and supersolutions

Mabel Cuesta Leon

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 4, page 591-608
  • ISSN: 0240-2963

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Cuesta Leon, Mabel. "Existence results for quasilinear problems via ordered sub and supersolutions." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.4 (1997): 591-608. <http://eudml.org/doc/73435>.

@article{CuestaLeon1997,
author = {Cuesta Leon, Mabel},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {-Laplacian; existence of maximal and minimal solutions; weak sub- and supersolutions; generalization of Kato's inequality},
language = {eng},
number = {4},
pages = {591-608},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Existence results for quasilinear problems via ordered sub and supersolutions},
url = {http://eudml.org/doc/73435},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Cuesta Leon, Mabel
TI - Existence results for quasilinear problems via ordered sub and supersolutions
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 4
SP - 591
EP - 608
LA - eng
KW - -Laplacian; existence of maximal and minimal solutions; weak sub- and supersolutions; generalization of Kato's inequality
UR - http://eudml.org/doc/73435
ER -

References

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  1. [1] Amann ( H.) .- Fixed Point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev.18 (1976), pp. 620-709. Zbl0345.47044MR415432
  2. [2] Amann ( H.) and Crandall ( M.G.) .- On existence theorems for semilinear elliptic boundary problems, Indiana Univ. Math. J.27 (1978), pp. 779-789. Zbl0391.35030MR503713
  3. [3] Boccardo ( L.), Murat ( F.) and Puel ( J.-P.) .— Résultats d'existence pour certains problèmes elliptiques quasilinéaires, Ann. Scuola Norm. Sup., Pisa, 11 (1984), pp. 213-235. Zbl0557.35051MR764943
  4. [4] Clément ( P.) and Sweers ( G.) .- Getting a solution between sub and supersolutions without monotone iterations, Rendiconti dell' Istituto di Matematica dell'Università de Trieste, 19 (1987), pp. 189-194. Zbl0687.35037MR988383
  5. [5] Diaz ( J.I.) .- Nonlinear P.D.E. and free boundaries, Vol. 1, Elliptic Equations, PitmanResearch Notes in Mathematics, 106 (1985). Zbl0595.35100MR853732
  6. [6] Dancer ( E.N.) and Sweers ( G.) .- On the existence of a maximal weak solutions for a semilinear elliptic equation, Diff. and Int. Equations2, n° 4 (1989), pp. 533-540. Zbl0732.35027MR996759
  7. [7] Deuel ( J.) and Hess ( P.) .— A criterion for the existence of solutions of nonlinear elliptic boundary value problems, Proc. Royal Soc. of Edinburgh A74 (1975), pp. 49-54. Zbl0331.35028MR440191
  8. [8] Hess ( P.) . — On a second order nonlinear elliptic boundary value problem, Non Linear Analysis (ed. by L. Cesari, R. Kannan and H. F. Weinberger), Academic Press, New York (1978), pp. 99-107. Zbl0464.35041MR499094
  9. [9] Kato ( T.) .— Schrodinger operators with singular potentials, Israel J. Math.13 (1972), pp. 135-148. Zbl0246.35025MR333833
  10. [10] Kura ( T.) .- The weak subsolution-supersolution method for second order quasilinear equations, Hiroshima Math. J.19 (1989), pp. 1-36. Zbl0735.35056MR1009660
  11. [11] Mitidieri ( E.) and Sweeps ( G.) .- Existence of a maximal solution for quasimonotone elliptic systems, Diff. and Int. Equations, 7, n° 6 (1994), pp. 1495-1510. Zbl0809.35027MR1269667
  12. [12] Nečas ( J.) .— Introduction to the Theory of NonLinear Elliptic Equations, John Wiley & Sons (1983). Zbl0643.35001
  13. [13] Tolksdorf ( P.) .— On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. P.D.E.8, n° 7 (1983), pp. 773-817. Zbl0515.35024MR700735

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