ON THE HALF-PLANE DIRICHLET PROBLEM FOR DIFFERENTIAL-DIFFERENCE ELLIPTIC EQUATIONS WITH SEVERAL NONLOCAL TERMS

The following Dirichlet problem is investigated: u(xx) + Sigma(k=1) (m) a(k)u(xx)(x + h(k), y) +u(yy) = 0, x is an element of(-infinity,+infinity), y is an element of(0,+infinity), u|(y=0) = u(0)(x), x is an element of(-infinity, +infinity), where the coefficients a(k) and h(k), k =1,m, are real parameters (no commensurability of the translations is assumed), while the boundary-value function u(0) is continuous and bounded. Such problems arise in various applications such as the multi-layer plates and envelopes theory, the diffusion processes theory (including biomathematical applications), models of nonlinear optics, etc.