On L w 2 -quasi-derivatives for solutions of perturbed general quasi-differential equations

Sobhy El-sayed Ibrahim

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 4, page 877-890
  • ISSN: 0011-4642

Abstract

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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 ] - λ w y = w f ( t , y [ 0 ] , ... , y [ n - 1 ] ) , t ∈ [ a , b ) provided that all r th quasi-derivatives of solutions of M [ y ] - λ w y = 0 and all solutions of its normal adjoint M + [ z ] - λ ¯ w z = 0 are in L w 2 ( a , b ) and under suitable conditions on the function f .

How to cite

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Ibrahim, Sobhy El-sayed. "On $L^2_w$-quasi-derivatives for solutions of perturbed general quasi-differential equations." Czechoslovak Mathematical Journal 49.4 (1999): 877-890. <http://eudml.org/doc/30532>.

@article{Ibrahim1999,
abstract = {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 $f$.},
author = {Ibrahim, Sobhy El-sayed},
journal = {Czechoslovak Mathematical Journal},
keywords = {quasi-differential operators; regular; singular; bounded and square integrable solutions; quasi-differential operators; regular; singular; bounded and square integrable solutions},
language = {eng},
number = {4},
pages = {877-890},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $L^2_w$-quasi-derivatives for solutions of perturbed general quasi-differential equations},
url = {http://eudml.org/doc/30532},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Ibrahim, Sobhy El-sayed
TI - On $L^2_w$-quasi-derivatives for solutions of perturbed general quasi-differential equations
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 877
EP - 890
AB - 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 $f$.
LA - eng
KW - quasi-differential operators; regular; singular; bounded and square integrable solutions; quasi-differential operators; regular; singular; bounded and square integrable solutions
UR - http://eudml.org/doc/30532
ER -

References

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