ON $L^2_W$ QUASI-DERIVATIVES FOR SOLUTIONS OF PERTURBED GENERAL QUASI-DIFFERENTIAL EQUATIONS
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Abstract
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equations of nth order with complex coefficients $M[y] -\lambda wy = w f(t, y^{[0]}, \cdots ,y^{[n- 1]})$, $t \in [a,b)$ provided that all $r$th quasi-derivatives of solutions of $M[y] -\lambda wy = 0$ and all solutions of its formal adjoint $M^+[z] -\lambda wz = 0$ are in $L _W^2(a, b)$ and under suitable conditions on the function $f$.
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