@article{RSMUP_2002__107__9_0, author = {Fiacca, Antonella and Matzakos, Nikolaos and Papageorgiou, Nikolaos S.}, title = {On nonlinear elliptic problems with discontinuities}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, volume = {108}, year = {2002}, pages = {9-33}, mrnumber = {1926198}, zbl = {1072.35072}, language = {en}, url = {http://dml.mathdoc.fr/item/RSMUP_2002__107__9_0} }
Fiacca, Antonella; Matzakos, Nikolaos; Papageorgiou, Nikolaos S. On nonlinear elliptic problems with discontinuities. Rendiconti del Seminario Matematico della Università di Padova, Tome 108 (2002) pp. 9-33. http://gdmltest.u-ga.fr/item/RSMUP_2002__107__9_0/
[1] Sobolev Spaces, Academic Press, New York (1975). | MR 450957 | Zbl 0314.46030
,[2] The dual variational principle and elliptic problems with discontinuities, J. Math. Anal. Appl, 140 (1989), pp. 363-373. | MR 1001862 | Zbl 0687.35033
- ,[3] Etude des Valeurs Propres et de la Resonance pour l'Operateur p-Laplacien, Ph. D. Thesis, Universite Libre de Bruxelles (1988).
,[4] Stongly nonlinear elliptic problems near resonance: A variational approch, Comm. Partial Diff. Equations, 15 (1990), pp. 1141-1159. | MR 1070239 | Zbl 0715.35029
- ,[5] 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] Some discontinuous problems with a quasilinear operator, J. Math. Anal. Appl, 187 (1994), pp. 1052-1072. | MR 1298837 | Zbl 0815.35018
- ,[7] A generalization of Fredholm alternative for nonilinear differential operatos, Nonlin. Anal., 10 (1986), pp. 1083-1103. | MR 857742 | Zbl 0623.34031
- - - ,[8] 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] 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] Existence results for perturbations of the p-Laplacian, Nonlin. Anal., 24 (1995), pp. 409-418. | MR 1312776 | Zbl 0818.35029
- ,[11] A note on a nonresonance condition for a quasilinear elliptic problem, Nonlin. Anal, 22 (1994), pp. 229-234. | MR 1258959 | Zbl 0816.35031
- ,[12] Maximum and comparison principles for operators involving the p-Laplacian, J. Math. Appl., 218 (1998), pp. 49-65. | MR 1601841 | Zbl 0897.35015
- ,[13] Elliptic Partial Equations of Second Order, Springer Verlag, New York (2nd edition) (1983).
- ,[14] Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997). | MR 1485775 | Zbl 0887.47001
- ,[15] Handbook of Multivalued Analysis. Volume II: Applications, Kluwer, Dordrecht, The Netherlands (2000). | MR 1741926 | Zbl 0943.47037
- ,[16] Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968). | MR 244627 | Zbl 0164.13002
- ,[17] Nonlinear petrubations of linear elliptic boundary value problems at resonance, J. Math. Mech, 19 (1970), pp. 609-623. | MR 267269 | Zbl 0193.39203
- ,[18] Multiple solutions of semilinear elliptic problems at resonance, Nonlin. Anal., 24 (1995), pp. 1049-1059. | MR 1321744 | Zbl 0832.35048
- - ,[19] Boundary regularity for solutions of degenerate elliptic equations, Nonlin Anal., 12 (1988), pp. 1203-1219. | MR 969499 | Zbl 0675.35042
,[20] On the equation div (NDxNp22 Dx)1lNxNp22 x40, Proc. AMS, 109 (1991), pp. 157-164. | MR 1007505 | Zbl 0714.35029
,[21] Discontinuous semilinear differential equations and multiple valued maps, Proc. AMS, 64 (1977), pp. 277-282. | MR 442453 | Zbl 0413.35031
,[22] A general approach to semilinear elliptic boundary value problems at resonance, Diff. and Inegral Eqns-to appear. | Zbl 0829.35039
- ,[23] Maximal and minimal solutions of elliptic equaitons with discontinuouis nonlinearities, Math. Z., 163 (1978), pp. 238-249. | MR 513729 | Zbl 0403.35036
,[24] A strong maximum principle for some quasilinear elliptic equations, Applied math. Optim., 12 (1984), pp. 191-202. | MR 768629 | Zbl 0561.35003
,[25] Nonlinear Functional Analysis and its Applications II, Springer Verlag, New York (1990). | MR 816732 | Zbl 0684.47029
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