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We prove new existence results for linearly coupled system of wave and beam equations. The main concept is the matrix spectrum which is a natural extension of standard definition. Using invariant subspaces together with degree theoretic argument we obtain information about the range of the abstract operator.
The paper is concerned with a global bifurcation result for equations whose principal parts are anisotropic -Laplace-like operators. Using an abstract bifurcation result for equations with multivalued operators in Banach spaces together with topological degree calculations, we show the Rabinowitz alternative for the bifurcating branches.