2001Luminy conference on Quasilinear Elliptic and Parabolic Equations
and Systems
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 4752.
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
email: boccardo@mat.uniroma1.it 
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