Principal eigenvalues for indefinite-weight elliptic problems in 𝑅ⁿ

Allegretto, W.

doi:10.1090/S0002-9939-1992-1098396-9

Principal eigenvalues for indefinite-weight elliptic problems in $\textbf {R}^ n$
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Proc. Amer. Math. Soc. 116 (1992), 701-706 Request permission

Abstract:

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.

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