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A global bifurcation for nonlinear elliptic equations involving nonhomogeneous operators of \(p(x)\)-Laplace type. (English) Zbl 1413.35061

Summary: We are concerned with the following nonlinear problem (Equation presented) subject to Dirichlet boundary condition, provided that \(\mu\) is not an eigenvalue of the \(p(x)\)-Laplacian. The aim of this paper is to study the structure of the set of weak solutions of nonlinear equations of \(p(x)\)-Laplace type, by applying a bifurcation result for nonlinear operator equations.

MSC:

35B32 Bifurcations in context of PDEs
35D30 Weak solutions to PDEs
35J60 Nonlinear elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
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