EXISTENCE OF SOLUTIONS OF THE BOUNDARY VALUE PROBLEM FOR THE DIFFUSION EQUATION WITH PIECEWISE CONSTANT ARGUMENTS

In this paper the boundary value problem (BVP) for diffusion equation with piecewise constant arguments is studied. By using the separation of variables method, the considered BVP is reduced to the investigation of the existence conditions of solutions of initial value problems for differential equation with piecewise constant arguments. Existence conditions of infinitely many solutions or emptiness for considered differential equation are established and explicit formula for these solutions are obtained. Several examples are given to illustrate the obtained results.