Potentiality conditions for partial differential equations with deviating arguments (Q2388000)

The author finds conditions under which the partial differential operator with deviating arguments \[ f(x,u_\alpha^{(k)}(x,t+\lambda \tau)), \quad k=0,\dots,l, \;| \alpha| = 0,\dots,s, \;\lambda = -1,0,1 \] is potential on a certain set with respect to the bilinear form \[ \langle v,g\rangle = \int_{t_1}^{t_2} \int_\Omega v(x,t)g(x,t_2-t)dxdt. \]