Article
MSC:
34A05,
34A25,
34B15,
34B25,
34C11,
34E10,
34E15,
34G10,
34M45,
47A55,
47E05 | MR 1746713 | Zbl 1015.34002
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Keywords:
quasi-differential operators; regular; singular; bounded and square integrable solutions
quasi-differential operators; regular; singular; bounded and square integrable solutions
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 $f$.
References:
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