# An elementary proof of Weyl's limit-classification

01 Apr 1989-Journal of The Australian Mathematical Society (Cambridge University Press (CUP))-Vol. 46, Iss: 2, pp 171-176

About: This article is published in Journal of The Australian Mathematical Society.The article was published on 1989-04-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Limit (mathematics) & Elementary proof.

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TL;DR: In this paper, the authors considered both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales and proved that the forward jump of at least one solution of this equation must be squarely integrable with respect to some multiple function which is of one sign and nonzero on the given time scale.

Abstract: In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at least one solution of this equation must be squarely integrable with respect to some multiple function which is of one sign and nonzero on the given time scale. Then using the obtained results for the single dynamic equation with several parameters, we investigate the number of the products of the squarely integrable solutions of the singular several equations with distributional potentials and several parameters. Mathematics Subject Classication (2010): 34B20, 34B24, 34B05, 34B40, 34N05. Key words : Dynamic equation, multiparameter eigenvalue problem, Weyl theory, distributional potential, time scales.

6 citations

### Cites background from "An elementary proof of Weyl's limit..."

...Das [18] showed the existence of the circle equation corresponding to the regular boundary condition (1....

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TL;DR: The Weyl–Titchmarsh theory for the fractional Sturm– Liouville equation is constructed using the Caputo and Riemann–Liouville fractional operators having the order is between zero and one.

Abstract: In this paper we construct the Weyl–Titchmarsh theory for the fractional Sturm–Liouville equation. For this purpose we used the Caputo and Riemann–Liouville fractional operators having the order is between zero and one.

5 citations

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01 Jan 1962

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44 citations

### "An elementary proof of Weyl's limit..." refers methods in this paper

...I t should be remarked here tha t this method is not only applicable to any higher even order differential equation, it avoids the whole lot of complications involved in dealing with the singular surfaces t h a t are to be associated wi th higher order equations, as in Everit t [1]....

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3 citations

### "An elementary proof of Weyl's limit..." refers background in this paper

...[3] An elementary proof of Weyl's limit-classification 173...

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