Czechoslovak Mathematical Journal, Vol. 49, No. 4, pp. 877-890, 1999

On $L^2_w$-quasi-derivatives for solutions of perturbed general quasi-differential equations

Sobhy El-sayed Ibrahim

Benha University, Faculty of Science Department of Mathematics, Benha 13518, Egypt

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 $f$.

Keywords: quasi-differential operators, regular, singular, bounded and square integrable solutions

Classification (MSC 1991): 34A05, 34B25, 34C11, 34E10, 34E15, 34G10, 47A55 and 47E05


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