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regulated functions; Perron-Stieltjes integral; Kurzweil integral; generalized differential equation; linear second order equation; distributional coefficients; existence; boundary value problem; numerical approximation; uniqueness; distribution
The paper deals with the linear differential equation (0.1) $(pu')'+q'u=f''$ with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).
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