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A criterion for compactness in Lp(ℝ) of the resolvent of the maximal general form Sturm–Liouville operator
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 3 / June 2016
- Published online by Cambridge University Press:
- 19 April 2016, pp. 483-508
- Print publication:
- June 2016
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We consider the equation
where
and
We assume that this equation is correctly solvable in Lp(ℝ). Under these assumptions, we study the problem of compactness of the resolvent
of the maximal continuously invertible Sturm–Liouville operator 
. Here
In the case p = 2, for the compact operator
, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.
and
of the maximal continuously invertible Sturm–Liouville operator 
. Here
, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.ON THE BEHAVIOUR OF EIGENVALUES ASSOCIATED WITH STURM–LIOUVILLE PROBLEMS ON SHRINKING DOMAINS
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 1 / February 2006
- Published online by Cambridge University Press:
- 02 February 2006, pp. 201-214
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