Geodesic
Linear distributional differential equations of the second order
Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 415-436

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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).
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).
DOI : 10.21136/MB.1994.126120
Classification : 34A12, 34A37, 34B05, 46F10, 46F99, 65J99
Keywords: regulated functions; Perron-Stieltjes integral; Kurzweil integral; generalized differential equation; linear second order equation; distributional coefficients; existence; boundary value problem; numerical approximation; uniqueness; distribution 
Tvrdý, Milan. Linear distributional differential equations of the second order. Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 415-436. doi: 10.21136/MB.1994.126120
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