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Principal eigenvalues for indefinite-weight elliptic problems in \(\mathbb{R}{}^ n\). (English) Zbl 0764.35031

Summary: We consider the problem \(-\Delta u=\lambda gu\) in \(R^ n\), \(u\to 0\) at \(\infty\) with \(g\) a function that changes sign. Under suitable growth conditions on \(g\) we show that this problem has an eigenvalue \(\lambda\) with a positive solution \(u\), as well as countably many other eigenvalues.

MSC:

35J20 Variational methods for second-order elliptic equations
35P15 Estimates of eigenvalues in context of PDEs
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