Abstract
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of nth order with complex coefficients M[y] − λwy = wf(t, y [0],... , y [n−1]), t ∈ [a, b) provided that all rth quasi-derivatives of solutions of M[y] − λwy = 0 and all solutions of its normal adjoint \(M^ + [z] - \bar \lambda wz = 0\) are in \(L_w^2 (a,b)\) and under suitable conditions on the function f.
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Ibrahim, S.ES. On \(L_w^2 \)-quasi-derivatives for solutions of perturbed general quasi-differential equations. Czechoslovak Mathematical Journal 49, 877–890 (1999). https://doi.org/10.1023/A:1022421605550
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DOI: https://doi.org/10.1023/A:1022421605550