Fiacca, Antonella; Matzakos, Nikolaos; Papageorgiou, Nikolaos S.
On nonlinear elliptic problems with discontinuities
Rendiconti del Seminario Matematico della Università di Padova, Tome 107 (2002) , p. 9-33
Zbl 1072.35072 | MR 1926198
URL stable : http://www.numdam.org/item?id=RSMUP_2002__107__9_0

Bibliographie

[1] R. Adams, Sobolev Spaces, Academic Press, New York (1975). MR 450957 | Zbl 0314.46030

[2] A. Ambrosetti - M. Badiale, The dual variational principle and elliptic problems with discontinuities, J. Math. Anal. Appl, 140 (1989), pp. 363-373. MR 1001862 | Zbl 0687.35033

[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] A. Anane - J. P. Gossez, Stongly nonlinear elliptic problems near resonance: A variational approch, Comm. Partial Diff. Equations, 15 (1990), pp. 1141-1159. MR 1070239 | Zbl 0715.35029

[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. MR 1417265 | Zbl 0854.35081

[6] D. Arcoya - M. Calahorrano, Some discontinuous problems with a quasilinear operator, J. Math. Anal. Appl, 187 (1994), pp. 1052-1072. MR 1298837 | Zbl 0815.35018

[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. MR 857742 | Zbl 0623.34031

[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. MR 1383891 | Zbl 0832.35039

[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. MR 614246 | Zbl 0487.49027

[10] D. Costa - C. Magalhaes, Existence results for perturbations of the p-Laplacian, Nonlin. Anal., 24 (1995), pp. 409-418. MR 1312776 | Zbl 0818.35029

[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. MR 1258959 | Zbl 0816.35031

[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. MR 1601841 | Zbl 0897.35015

[13] D. Gilbarg - N. Trundinger, Elliptic Partial Equations of Second Order, Springer Verlag, New York (2nd edition) (1983).

[14] S. Hu - N. S. Papageorgiou, Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997). MR 1485775 | Zbl 0887.47001

[15] S. Hu - N. S. Papageorgiou, Handbook of Multivalued Analysis. Volume II: Applications, Kluwer, Dordrecht, The Netherlands (2000). MR 1741926 | Zbl 0943.47037

[16] O. Ladyzhenskaya - N. Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968). MR 244627 | Zbl 0164.13002

[17] E. M. Landesman - A. Lazer, Nonlinear petrubations of linear elliptic boundary value problems at resonance, J. Math. Mech, 19 (1970), pp. 609-623. MR 267269 | Zbl 0193.39203

[18] E. M. Landesman - S. Robinson - A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlin. Anal., 24 (1995), pp. 1049-1059. MR 1321744 | Zbl 0832.35048

[19] G. M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlin Anal., 12 (1988), pp. 1203-1219. MR 969499 | Zbl 0675.35042

[20] P. Lindqvist, On the equation div (NDxNp22 Dx)1lNxNp22 x40, Proc. AMS, 109 (1991), pp. 157-164. MR 1007505 | Zbl 0714.35029

[21] J. Rauch, Discontinuous semilinear differential equations and multiple valued maps, Proc. AMS, 64 (1977), pp. 277-282. MR 442453 | Zbl 0413.35031

[22] S. Robinson - E. M. Landesman, A general approach to semilinear elliptic boundary value problems at resonance, Diff. and Inegral Eqns-to appear. Zbl 0829.35039

[23] C. Stuart, Maximal and minimal solutions of elliptic equaitons with discontinuouis nonlinearities, Math. Z., 163 (1978), pp. 238-249. MR 513729 | Zbl 0403.35036

[24] J. L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Applied math. Optim., 12 (1984), pp. 191-202. MR 768629 | Zbl 0561.35003

[25] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer Verlag, New York (1990). MR 816732 | Zbl 0684.47029