Calculus of Variations and Geometric Measure Theory
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A. Dall'Aglio - V. De Cicco - D. Giachetti - J. P. Puel

Existence of bounded solutions for nonlinear elliptic equations in unbounded domains

created on 21 May 2003
modified by decicco on 15 Dec 2005


Published Paper

Inserted: 21 may 2003
Last Updated: 15 dec 2005

Journal: NoDEA-Nonlinear Differential Equations and Applications
Year: 2004


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.


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