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Nonlinear eigenvalues and bifurcation problems for Pucci’s operators. (English) Zbl 1205.35087

Summary: In this paper we extend existing results concerning generalized eigenvalues of Pucci’s extremal operators. In the radial case, we also give a complete description of their spectrum, together with an equivalent of Rabinowitz’s Global Bifurcation Theorem. This allows us to solve nonlinear equations involving Pucci’s operators.

MSC:

35J60 Nonlinear elliptic equations
35P05 General topics in linear spectral theory for PDEs
35B32 Bifurcations in context of PDEs
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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