Geodesic
On $L^2_w$-quasi-derivatives for solutions of perturbed general quasi-differential equations
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 877-890 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $M[y] - \lambda wy = wf (t, y^{[0]}, \ldots ,y^{[n-1]})$, $t\in [a,b)$ 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 $f$.
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 $f$.
Classification : 34A05, 34A25, 34B15, 34B25, 34C11, 34E10, 34E15, 34G10, 34M45, 47A55, 47E05
Keywords: quasi-differential operators; regular; singular; bounded and square integrable solutions 
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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, Tome 49 (1999) no. 4, pp. 877-890. http://geodesic.mathdoc.fr/item/CMJ_1999_49_4_a18/

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