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Eigenvalue problems of the form x” = −λf(x+ ) + μg(x− ), x‘(a) = 0, x' (b) = 0 are considered. We are looking for (λ,μ) such that the problem (i), (ii) has a nontrivial solution. This problem generalizes the famous Fučík problem for piece‐wise linear equations. In our considerations functions f and g may be nonlinear. Consequently spectra may differ essentially from those for the Fučík equation.
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