Inserted: 21 may 2003
Last Updated: 15 dec 2005
Journal: NoDEA-Nonlinear Differential Equations and Applications
In this paper we study the existence of bounded weak solutions in unbounded domains for some nonlinear Dirichlet problems. The principal part of the operator behaves like the $p$-laplacian operator, and the lower order terms, which depend on the solution $u$ and its gradient $\D u$, have a power growth of order $p-1$ with respect to these variables, while they are bounded in the $x$ variable. The source term belongs to a Lebesgue space with a prescribed asymptotic behaviour at infinity.