Some properties of the Sturm-Liouville operator in L_p(R)

N. A. Chernyavskaya; L. A. Shuster

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Some properties of the Sturm-Liouville operator in L_p(R)

N. A. Chernyavskaya·L. A. Shuster

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Abstract

We consider the boundary problem -y''(x)+q(x)y(x)=f(x), lim_{|x|\to\infty}y^{(i)}(x)=0, i=0,1, where f(x)\in L_p(R), p\in[1,\infty], 1\le q(x)\in L_1^{\loc}(R). For this boundary problem we obtain: 1) necessary and sufficient conditions for unique solvability and a priori properties of the solution; 2) a criterion for the resolvent to be compact in L_p(R), and some a priori properties of the spectrum.

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BibTeX RIS

N. A. Chernyavskaya, L. A. Shuster. 1998-09-03. Some properties of the Sturm-Liouville operator in L_p(R). https://arxiv.org/abs/math/9809012

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