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International Journal of Differential Equations
Volume 2011, Article ID 453727, 18 pages
http://dx.doi.org/10.1155/2011/453727
Research Article

Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity

Department of Mathematics, University of Salerno, 84084 Fisciano, Italy

Received 4 May 2011; Accepted 8 September 2011

Academic Editor: Julio Rossi

Copyright © 2011 G. Galise and A. Vitolo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We deal with fully nonlinear second-order equations assuming a superlinear growth in u with the aim to generalize previous existence and uniqueness results of viscosity solutions in the whole space without conditions at infinity. We also consider the solvability of the Dirichlet problem in bounded and unbounded domains and show a blow-up result.