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We consider a well-posed eigenvalue problem on $(a,0)$, depending on acontinuous function $m$. The boundary conditions in the points $a,0$ aredepending on the eigenvalues. We divide $(a,0)$ into small intervals andapproximate the function $m$ by a simple (step) function $m_S$, constant oneach small interval. The eigenfunctions corresponding to $m_S$ do not exist.

A non-existence result due to small perturbations in an eigenvalue problem