| Title:
|
On $L^2_w$-quasi-derivatives for solutions of perturbed general quasi-differential equations (English) |
| Author:
|
Ibrahim, Sobhy El-sayed |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
877-890 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of $n$th order with complex coefficients $M[y] - \lambda wy = wf (t, y^{[0]}, \ldots ,y^{[n-1]})$, $t\in [a,b)$ provided that all $r$th quasi-derivatives of solutions of $M[y] - \lambda w y = 0$ and all solutions of its normal adjoint $M^+[z] - \bar{\lambda } w z = 0$ are in $L^2_w (a,b)$ and under suitable conditions on the function $f$. (English) |
| Keyword:
|
quasi-differential operators |
| Keyword:
|
regular |
| Keyword:
|
singular |
| Keyword:
|
bounded and square integrable solutions |
| MSC:
|
34A05 |
| MSC:
|
34A25 |
| MSC:
|
34B15 |
| MSC:
|
34B25 |
| MSC:
|
34C11 |
| MSC:
|
34E10 |
| MSC:
|
34E15 |
| MSC:
|
34G10 |
| MSC:
|
34M45 |
| MSC:
|
47A55 |
| MSC:
|
47E05 |
| idZBL:
|
Zbl 1015.34002 |
| idMR:
|
MR1746713 |
| . |
| Date available:
|
2009-09-24T10:28:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127537 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[8] M.N. Naimark: Linear Differential Operators.(G.I.T.T.L., Moscow, 1954), Ungar, New York, Vol. I (1967), Vol. II (1968). Zbl 0227.34020 |
| Reference:
|
[9] Sobhy El-sayed Ibrahim: Problems associated with differential operators.Ph.D. thesis (1989), Faculty of Sciences, Department of Mathematics, Benha University, Egypt. |
| Reference:
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[10] Sobhy El-sayed Ibrahim: Boundedness for solutions of general ordinary quasi-differential equations.Journal of the Egyptian Mathematical Society 2 (1994), 33–44. Zbl 0818.34019, MR 1319065 |
| Reference:
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[11] Sobhy El-sayed Ibrahim: The spectra of well-posed operators.Proc. Royal Soc. of Edinburgh 124A (1995), 1331–1348. MR 1363006 |
| Reference:
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| Reference:
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[13] D. Willett and J.S.W. Wong: On the discrete analogues of some generalizations of Gronwall’s inequality.Monatsh. Math. 69 (1965), 362–367 MR 32 $\ne $ 2644. MR 0185175, 10.1007/BF01297622 |
| Reference:
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| Reference:
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| Reference:
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[16] A. Zettl: Perturbation of the limit circle case.Quart. J. Math., Oxford (3) 26 (1975), 355–360. Zbl 0325.34022, MR 0470315, 10.1093/qmath/26.1.355 |
| Reference:
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[17] A. Zettl: Formally self-adjoint quasi-differential operators.Rocky Mountain Journal of Mathematics (3) 5 (1975), 453–474. MR 0379976, 10.1216/RMJ-1975-5-3-453 |
| . |
