Limit Point Criteria for Differential Equations, II

Don Hinton

doi:10.4153/CJM-1974-035-7

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We consider here singular differential operators, and for convenience the finite singularity is taken to be zero. One operator discussed is the operator L defined by

where q0 > 0 and the coefficients qt are real, locally Lebesgue integrable functions defined on an interval (a, b). For a given positive, continuous weight function h, conditions are given on the functions qi for which the number of linearly independent solutions y of L(y) = λhy (Re λ = 0) satisfying.

References

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3. Naimark, M. A., Linear differential operators, Part II (Ungar, New York, 1968).Google Scholar

4. Walker, P. W., Asymptotic s for a class of weighted eigenvalue problems, Pacific J. Math. 40 (1972), 501–510.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Atkinson, F. V. 1975. 11.—Limit-n Criteria of Integral Type. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 73, Issue. , p. 167.

Hinton, Don 1977. Strong limit-point and Dirichlet criteria for ordinary differential expressions of order 2n. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 76, Issue. 4, p. 301.

Hinton, Don B 1977. On the eigenfunction expansions of singular ordinary differential equations. Journal of Differential Equations, Vol. 24, Issue. 2, p. 282.

Hinton, Don B. and Lewis, Roger T. 1979. Singular differential operators with spectra discrete and bounded below. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 84, Issue. 1-2, p. 117.

Kurss, H. and Meyer, G. 1981. Limit-point (LP) criteria for real symmetric differential expressions of order 2n. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 88, Issue. 3-4, p. 203.

Ahlbrandt, Calvin D Hinton, Don B and Lewis, Roger T 1981. The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory. Journal of Mathematical Analysis and Applications, Vol. 81, Issue. 1, p. 234.

Ahlbrandt, Calvin D. Hinton, Don B. and Lewis, Roger T. 1981. Ordinary and Partial Differential Equations. Vol. 846, Issue. , p. 17.

Bradley, John S. Hinton, Don B. and Kauffman, Robert M. 1981. On the minimization of singular quadratic functional. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 87, Issue. 3-4, p. 193.

Ahlbrandt, Calvin D. Hinton, Don B. and Lewis, Roger T. 1982. Transformations of second order ordinary and partial difierential operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 92, Issue. 1-2, p. 31.

Frentzen, Hilbert 1988. LIMIT-POINT CRITERIA FOR SYMMETRIC AND J-SYMMETRIC QUASI-DIFFERENTIAL EXPRESSIONS OF EVEN ORDER WITH A POSITIVE DEFINITE LEADING COEFFICIENT. Quaestiones Mathematicae, Vol. 11, Issue. 2, p. 119.

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