USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 29-44.

Behaviour near zero and near infinity of solutions to elliptic equalities and inequalities

Marie-Françoise Bidaut-Véron

Here we consider elliptic equations and inequalities involving quasilinear operators in divergence form and nonlinear lower order terms:
$-{\rm div}\left(\cal{A}(x
,u,\nabla u)\right)\geq |x|^\sigma u^Q\quad
(Q greater than 0,\sigma \in \mathbb{R})$,
in dimension $N\geq 3$. We study the asymptotic behaviour of the solutions and give a priori estimate and non-existence results.

Published January 8, 2001.
Math Subject Classifications: 35J55, 35J60.
Key Words: A priori estimates, non-existence results, degenerate quasilinear inequalities.

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Marie-Françoise Bidaut-Véron
Laboratoire de Mathematiques et Physique Theorique
Faculte des Sciences et Techniques
Parc de Grandmont
F 37200 Tours France

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