(1) Dipartimento di Metodi e Modelli, Matematici per le Scienze Applicate, Università di Roma I La Sapienza, Via Antonio Scarpa 16, 00161 Roma, Italy;(2) Laboratoire de Mathématiques Appliquées, Université de Versailles St. Quentin, 45 Avenue des Etats Unis, 78035 Versailles Cedex, France
Abstract:
In this paper we study the existence of bounded weak solutions for some nonlinear Dirichlet problems in unbounded domains. 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 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.
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La Sapienza!["rdquo"]("/content/2gbk5n7blludag1v/xlarge8221.gif")
, Via Antonio Scarpa 16, 00161 Roma, Italy;(2) Laboratoire de Mathématiques Appliquées, Université de Versailles St. Quentin, 45 Avenue des Etats Unis, 78035 Versailles Cedex, France
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.