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A bifurcation result for equations with anisotropic \(p\)-Laplace-like operators. (English) Zbl 1003.58018

The main purpose of this paper is to establish a global bifurcation result for equations involving anisotropic \(p\)-Laplace type operators. This result generalizes in a nontrivial way the Rabinowitz global bifurcation theorem to equations whose operators are not necessarily compact perturbations of linear mappings. This framework contains the case where the principal operators are not in the classes \((S)\) or \((S)^+\). In the particular case of quasilinear operators of \(p\)-Laplace type it is established the existence of a bifurcation at the principal eigenvalue and that the corresponding bifurcation branch satisfies the Rabinowitz alternative.
The paper is well written and the proofs use various techniques involving monotone operators or topological degree arguments.

MSC:

58E35 Variational inequalities (global problems) in infinite-dimensional spaces
35J60 Nonlinear elliptic equations
58J55 Bifurcation theory for PDEs on manifolds
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