On the half-plane Dirichlet problem for differential-difference elliptic equations with several nonlocal terms

The following Dirichlet problem is investigated: uxx + Σm k=1 ak uxx(x + hk; y) + uyy = 0; x ∈ (-∞;+ ∞); y ∈ (0;+ ∞); u|y=0 = u0(x); x ∈ (-∞;+ ∞);, where the coefficients ak and hk = 1, m, are real parameters (no commensurability of the translations is assumed), while the boundary-value function u0 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. © EDP Sciences, 2017.