Smoothness of generalized solutions of the boundary-value problem for differential-difference equations with incommensurable shifts

The differential equation -(v-varepsilon Rv)"(t)=f_0(t), tin(0,d), with the boundary condition v(t)=0, tnotin(0,d), is considered. It is assumed that (Rv)(t)=sum_{j=1}^ma_jv(t+tau_j), tau_jinBbb R, f_0in L_2(0,d), 0<varepsilon<(2sum_{j=1}^m|a_j|)^{-1}, sum_{j=1}^mq_jtau_jneq d for all q_jinBbb Z, and there does not exist alpha_jinBbb Z such that sum_{j=1}^malpha_jtau_j=0 and sum_{j=1}^malpha_j^2neq0. A generalized solution is a function vin W_2^1 such that v-varepsilon Rvin W_2^2 and the differential equation is satisfied. It is proved that the set of discontinuities of v', where v is a generalized solution, is dense in (0,d).