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Generalized eigenvalues for fully nonlinear singular or degenerate operators in the radial case. (English) Zbl 1191.35200
In this article, the generalized eigenvalues for general operators fully nonlinear singular or degenerate homogeneous of degree \(1+\alpha\) with \(\alpha>-1\) are considered on a bounded domain \(\Omega\) in \(\mathbb R^N\). Specifically, the radial case for the operator \(F(Du,D^2u)= |\nabla u|^\alpha {\mathcal M}_{a,A}(D^2u)\) is treated, where \({\mathcal M}_{a,A}\) is the Pucci’s operator \({\mathcal M}_{a,A} (M) = A \operatorname{tr}(M^+)- a \operatorname{tr}(M^-)\) with \(a \leq A\). The authors prove the existence of a denumerable set of eigenvalues which are simple and isolated, and some continuity results for the eigenvalues with respect to the parameters \(\alpha, a, A\).

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J25 Boundary value problems for second-order elliptic equations
35J60 Nonlinear elliptic equations
35P15 Estimates of eigenvalues in context of PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs