Iterative methods for quasilinear hyperbolic systems in the first canonic form

On the Cauchy Problem for Quasilinear Hyperbolic Systems of Partial Differential-Functional Equations of the First Order

“…Any function z € K(P,x,Q) satisfies (2). This function is a solution of (1), (2) if it satisfies the system (1) a.e.…”

Multipoint problem for typeless systems of differential equations with constant coefficients

“…Multipoint problems for first-order quasilinear hyperbolic systems were studied in [14][15][16][17][18], for linear evolution systems, they were studied in [19][20][21], and for systems of linear differential and pseudodifferential equations of arbitrary order, they were studied in [22,23]. For operator-differential equations, problems with multipoint conditions were studied in [24,25].…”

Unbounded Solutions of Quasilinear Differential-Functional Equations

“…In this paper we give sufficient conditions for the existence and uniqueness of unbounded classical solutions of (1), (2). The method used in this paper is based on results due to P. Bassanini and L. Cesari for solutions in the sense "almost everywhere" of systems which are not functional (see [1]- [4]).…”