The eigenvalue problem for a singular quasilinear elliptic equation
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We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a C1,α(Ω) eigenfunction which is positive and unique (up to a multiplicative constant), that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
CitationXuan, B. (2004). The eigenvalue problem for a singular quasilinear elliptic equation. Electronic Journal of Differential Equations, 2004(16), pp. 1-11.
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