The concept of eigenvalue has recently been extended to a large class of fully-nonlinear operators, here for fully-nonlinear operators in non divergence form that present singularities and degeneracies similar to the p-Laplacian we prove that in the radial case the eigenfunction is simple.
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Isabeau Birindelli, F. Demengel, Uniqueness of the First Eigenfunction for Fully Nonlinear Equations: the Radial Case. Z. Anal. Anwend. 29 (2010), no. 1, pp. 77–90DOI 10.4171/ZAA/1398