On uniqueness for nonlinear elliptic equation involving the Pucci's extremal operator |
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Authors: | Patricio L Felmer Alexander Quaas |
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Institution: | a Departamento de Ing. Matemática, F.C.F.M. Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile b Departamento de Matemática, Universidad Santa María Casilla, V-110, Avda. España 1680, Valparaíso, Chile c Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
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Abstract: | In this article we study uniqueness of positive solutions for the nonlinear uniformly elliptic equation in RN, limr→∞u(r)=0, where denotes the Pucci's extremal operator with parameters 0<λ?Λ and p>1. It is known that all positive solutions of this equation are radially symmetric with respect to a point in RN, so the problem reduces to the study of a radial version of this equation. However, this is still a nontrivial question even in the case of the Laplacian (λ=Λ). The Pucci's operator is a prototype of a nonlinear operator in no-divergence form. This feature makes the uniqueness question specially challenging, since two standard tools like Pohozaev identity and global integration by parts are no longer available. The corresponding equation involving is also considered. |
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Keywords: | primary 35J60 secondary 34B15 35B33 35B45 |
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