Thsi paper is concerned with a positive solution u of the non#x2013;homogeneous p#x2013;Laplacian equation in an open, bounded, connected subset #x3A9; of Rnwith C2boundary. We assume that u verifies overdetermined boundary conditions and we prove that of us has only one critial point #x3A9; then#x3A9; is a ball and u is radially symmetric; to prove this result we use the moving planes method introduced by J.Serrien. Using the same technique we also prove that the result is stable in the following sense: the boundary of #x3A9; tends to the boundary of a sphere as the diameter of the critical set u tends to 0.
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