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On the generalized spectrum for second-order elliptic systems. (English) Zbl 0652.35084

The author studies some properties of the set of \((\lambda_ 1,\lambda_ 2)\in {\mathbb{R}}^ 2\) such that the homogeneous Dirichlet problem \(L_ iu_ i=\lambda_ i(a_{i1}u_ 1+a_{i2}u_ 2)\), \(i=1,2\), has a non trivial solution. The \(L_ i\) are self-adjoint second order strongly elliptic operators and the matrix \((a_{ij})\) is for most results positive definite. All the coefficients are smooth. The techniques used are perturbation theory, implicit function theorem and min-max characterization of eigenvalues.
Reviewer: G.Geymonat

MSC:

35P05 General topics in linear spectral theory for PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B20 Perturbations in context of PDEs
35B32 Bifurcations in context of PDEs
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