One class of solutions of Volterra equations with regular singularity
The Volterra integral equation of the second order with a regular singularity is considered. Under the conditions that a kernel K(x,t) is a real matrix function of order n×n with continuous partial derivatives up to order N+1 inclusively and K(0,0) has complex eigenvalues ν±i μ (ν>0), it is shown that if ν>2|‖K|‖ C -N-1, then a given equation has two linearly independent solutions.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 3, pp 467-476.
Citation Example: Krein S. G., Sapronov I. V. One class of solutions of Volterra equations with regular singularity // Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 424–432.