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| We consider Sturm-Liouville problem for the quasilinear second order equation with weights on finite or, possibly, infinite interval. We prove that conditions on weights, which are equivalent to the compactness of the embedding of certain weigted Sobolev and Lebesgue spaces, are also equivalent to the fact that the eigenvalues and eigenfunctions have the usual properties as those for a "standard" Sturm-Liouville problem on a finite interval. Some consequences for the radial problem on the entire R^N will be discussed as well. This is a joint work with Komil Kuliev and it was published in Bull. Belg. Math. Soc. Simon Stevin 2012. |
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