Solvability of the Goursat problem in quadratures

We find new variants of Goursat problem solution in quadratures on the basis of the combination of the Riemann method and the cascade integration. The results are applied to two Volterra equations with particular integrals. © 2013 Allerton Press, Inc

One approach to the solution of volterra integral equations with degenerate kernels

We propose a technique that in certain cases allows one to solve the considered equations in an explicit form. © 2011 Allerton Press, Inc

On Conditions of Solvability of the Goursat Problem for Generalized Aller Equation

© 2018, Allerton Press, Inc. In terms of coefficients of an equation under consideration, we derive 16 variants of collections of conditions of resolvability of this equation in quadratures. Every collection consists of three identities that interconnect five coefficients appearing in left-hand side of an equation

Solvability of the Goursat problem in quadratures

We find new variants of Goursat problem solution in quadratures on the basis of the combination of the Riemann method and the cascade integration. The results are applied to two Volterra equations with particular integrals. © 2013 Allerton Press, Inc

One approach to the solution of volterra integral equations with degenerate kernels

We propose a technique that in certain cases allows one to solve the considered equations in an explicit form. © 2011 Allerton Press, Inc

Solvability of the Goursat problem in quadratures

We find new variants of Goursat problem solution in quadratures on the basis of the combination of the Riemann method and the cascade integration. The results are applied to two Volterra equations with particular integrals. © 2013 Allerton Press, Inc

One approach to the solution of volterra integral equations with degenerate kernels

We propose a technique that in certain cases allows one to solve the considered equations in an explicit form. © 2011 Allerton Press, Inc

One approach to the solution of volterra integral equations with degenerate kernels

We propose a technique that in certain cases allows one to solve the considered equations in an explicit form. © 2011 Allerton Press, Inc