Unbounded Principal Eigenfunctions for Problems on all lR
نویسندگان
چکیده
We investigate the existence of principal eigenvalues, i.e., values of λ for which the corresponding eigenfunction is positive, for the problem −∆u(x) = λg(x)u(x) for x ∈ lR where g is a smooth function which may change sign, Unlike most previous studies the eigenfunction is not required to → 0 as |x| → ∞. It is shown that there may exist a closed interval of principal eigenvalues [λ∗, λ ] and sufficient conditions are given to ensure that principal eigenfunctions → 0 as |x| → ∞ if and only if λ = λ or λ∗.
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