Marynetz V. V.
Some approaches to the construction of approximate solutions of the generalized Goursat problem for systems of certain quasilinear partial differential equations with deviating argument
Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1667–1675
We construct and investigate monotone and alternating rapidly convergent two-sided methods for the approximate integration of the generalized Goursat problem, prove the existence and uniqueness of its regular solution, establish theorems on differential inequality and comparison, and obtain sufficient conditions for the existence of solutions of the indicated problem of fixed sign in a given domain.
On a mixed problem for systems of definite quasilinear partial differential equations with deviating argument
Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1581–1585
For a mixed problem for a system of definite quasilinear pseudoparabolic equations with deviating argument, we prove a theorem on differential inequalities and existence of a unique regular solution and a comparison theorem and give sufficient conditions of existence of solutions with constant sign.