On nonlinear elliptic problems with discontinuities

Antonella Fiacca; Nikolaos Matzakos; Nikolaos S. Papageorgiou

Rendiconti del Seminario Matematico della Università di Padova (2002)

  • Volume: 107, page 9-33
  • ISSN: 0041-8994

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Fiacca, Antonella, Matzakos, Nikolaos, and Papageorgiou, Nikolaos S.. "On nonlinear elliptic problems with discontinuities." Rendiconti del Seminario Matematico della Università di Padova 107 (2002): 9-33. <http://eudml.org/doc/108588>.

@article{Fiacca2002,
author = {Fiacca, Antonella, Matzakos, Nikolaos, Papageorgiou, Nikolaos S.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {9-33},
publisher = {Seminario Matematico of the University of Padua},
title = {On nonlinear elliptic problems with discontinuities},
url = {http://eudml.org/doc/108588},
volume = {107},
year = {2002},
}

TY - JOUR
AU - Fiacca, Antonella
AU - Matzakos, Nikolaos
AU - Papageorgiou, Nikolaos S.
TI - On nonlinear elliptic problems with discontinuities
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2002
PB - Seminario Matematico of the University of Padua
VL - 107
SP - 9
EP - 33
LA - eng
UR - http://eudml.org/doc/108588
ER -

References

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  1. [1] R. ADAMS, Sobolev Spaces, Academic Press, New York (1975). Zbl0314.46030MR450957
  2. [2] A. AMBROSETTI - M. BADIALE, The dual variational principle and elliptic problems with discontinuities, J. Math. Anal. Appl, 140 (1989), pp. 363-373. Zbl0687.35033MR1001862
  3. [3] A. ANANE, Etude des Valeurs Propres et de la Resonance pour l’Operateur p-Laplacien, Ph. D. Thesis, Universite Libre de Bruxelles (1988). 
  4. [4] A. ANANE - J. P. GOSSEZ, Stongly nonlinear elliptic problems near resonance: A variational approch, Comm. Partial Diff. Equations, 15 (1990), pp. 1141-1159. Zbl0715.35029MR1070239
  5. [5] A. ANANE - N. TSOULI, On the second eigenvalue of the p-Laplacian, in Nonlinear Partial Differential Equations, eds. A. Benkirane - J.-P. Gossez, Pitman Research Notes in Math, Vol. 343, Longman, Harlow, UK (1996), pp. 1-9. Zbl0854.35081MR1417265
  6. [6] D. ARCOYA - M. CALAHORRANO, Some discontinuous problems with a quasilinear operator, J. Math. Anal. Appl, 187 (1994), pp. 1052-1072. Zbl0815.35018MR1298837
  7. [7] L. BOCCARDO - P. DRABEK - D. GIACHETTI - M. KUCERA, A generalization of Fredholm alternative for nonilinear differential operatos, Nonlin. Anal., 10 (1986), pp. 1083-1103. Zbl0623.34031MR857742
  8. [8] S. CARL - H. DIETRICH, The weak upper and lower solution methods for quasilinear elliptic equations with generalized subdifferentiable petrubations, Appl. Anal., 56 (1995), pp. 263-278. Zbl0832.35039MR1383891
  9. [9] K.-C. CHANG, Variational methods for nondifferentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), pp. 102-129. Zbl0487.49027MR614246
  10. [10] D. COSTA - C. MAGALHAES, Existence results for perturbations of the p-Laplacian, Nonlin. Anal., 24 (1995), pp. 409-418. Zbl0818.35029MR1312776
  11. [11] A. EL HACHIMI - J.-P. GOSSEZ, A note on a nonresonance condition for a quasilinear elliptic problem, Nonlin. Anal, 22 (1994), pp. 229-234. Zbl0816.35031MR1258959
  12. [12] J. GARCIA MELIAN- J. SABINA DE LIS, Maximum and comparison principles for operators involving the p-Laplacian, J. Math. Appl., 218 (1998), pp. 49-65. Zbl0897.35015MR1601841
  13. [13] D. GILBARG - N. TRUNDINGER, Elliptic Partial Equations of Second Order, Springer Verlag, New York (2nd edition) (1983). 
  14. [14] S. HU - N. S. PAPAGEORGIOU, Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997). Zbl0887.47001MR1485775
  15. [15] S. HU - N. S. PAPAGEORGIOU, Handbook of Multivalued Analysis. Volume II: Applications, Kluwer, Dordrecht, The Netherlands (2000). Zbl0943.47037MR1741926
  16. [16] O. LADYZHENSKAYA - N. URALTSEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968). Zbl0164.13002MR244627
  17. [17] E. M. LANDESMAN - A. LAZER, Nonlinear petrubations of linear elliptic boundary value problems at resonance, J. Math. Mech, 19 (1970), pp. 609-623. Zbl0193.39203MR267269
  18. [18] E. M. LANDESMAN - S. ROBINSON - A. RUMBOS, Multiple solutions of semilinear elliptic problems at resonance, Nonlin. Anal., 24 (1995), pp. 1049-1059. Zbl0832.35048MR1321744
  19. [19] G. M. LIEBERMAN, Boundary regularity for solutions of degenerate elliptic equations, Nonlin Anal., 12 (1988), pp. 1203-1219. Zbl0675.35042MR969499
  20. [20] P. LINDQVIST, On the equation div (NDxNp22 Dx)1lNxNp22 x40, Proc. AMS, 109 (1991), pp. 157-164. Zbl0714.35029MR1007505
  21. [21] J. RAUCH, Discontinuous semilinear differential equations and multiple valued maps, Proc. AMS, 64 (1977), pp. 277-282. Zbl0413.35031MR442453
  22. [22] S. ROBINSON - E. M. LANDESMAN, A general approach to semilinear elliptic boundary value problems at resonance, Diff. and Inegral Eqns-to appear. Zbl0829.35039
  23. [23] C. STUART, Maximal and minimal solutions of elliptic equaitons with discontinuouis nonlinearities, Math. Z., 163 (1978), pp. 238-249. Zbl0403.35036MR513729
  24. [24] J. L. VAZQUEZ, A strong maximum principle for some quasilinear elliptic equations, Applied math. Optim., 12 (1984), pp. 191-202. Zbl0561.35003MR768629
  25. [25] E. ZEIDLER, Nonlinear Functional Analysis and its Applications II, Springer Verlag, New York (1990). Zbl0684.47029MR816732

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