Ufa Mathematical Journal
    Volume 6, Number 4, pp. 60-67

    Generalized solutions and Euler-Darboux transformations

    Verevkin I.V.


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    We introduce Euler-Darboux transformation for non-homogeneous differential equations with the right-hand side being a generalized function. As an example, we construct the fundamental solutions for Klein-Gordon-Fock and Schr\"odinger equations with variable coefficients describing a particle in external scalar field.