2001-Luminy conference on Quasilinear Elliptic and Parabolic Equations and Systems
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 47-52.

### A remark on some nonlinear elliptic problems Lucio Boccardo

Abstract:
We shall prove an existence result of solutions for the

with right hand side in . The features of the equation are that no restrictions on the growth of the function with respect to are assumed and that with respect to is monotone, but not strictly monotone. We overcome the difficulty of the uncontrolled growth of thanks to a suitable definition of solution (similar to the one introduced in [1] for the study of the Dirichlet problem in ) and the difficulty of the not strict monotonicity thanks to a technique (the -version of Minty's Lemma) similar to the one used in [5].

Published October 21, 2002.
Subject lassfications: 35J60, 35J65, 35J70.
Key words: Dirichlet problem in , uncontrolled growth.

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 Lucio Boccardo Dipartimento di Matematica Universita di Roma I Piazza A. Moro 2, 00185 Roma, Italia e-mail: boccardo@mat.uniroma1.it