Complex oscillations of non-definite Sturm-Liouville problems, II
We correct and update a result of R. G. D. Richardson [Amer. J. Math. 40(1918), 283–316] dealing with the separation of zeros of the real and imaginary parts of non-real eigenfunctions of non-definite Sturm–Liouville eigenvalue problems. We then extend it to the case where the weight function is all...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Sturm-Liouville probléma, Oszcilláció |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.54 |
| Online Access: | http://acta.bibl.u-szeged.hu/88934 |
| Tartalmi kivonat: | We correct and update a result of R. G. D. Richardson [Amer. J. Math. 40(1918), 283–316] dealing with the separation of zeros of the real and imaginary parts of non-real eigenfunctions of non-definite Sturm–Liouville eigenvalue problems. We then extend it to the case where the weight function is allowed to be identically zero on a subinterval that excludes the end-points and study the behavior of the zeros of the real and imaginary parts when the end-points are included. Examples are given illustrating the sharpness of the results along with open questions. |
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| Terjedelem/Fizikai jellemzők: | 14 |
| ISSN: | 1417-3875 |