Nonlinear elliptic equation with deviating arguments (Q2795684)

In this paper, existence and uniqueness results are established for the following nonlinear elliptic equation with a deviating argument: NEWLINE\[NEWLINE -\sum_{i,j=1}^N \frac{\partial}{\partial x_j}\left(a_{i,j}(x,u(\theta(x)))\frac{\partial u}{\partial x_i}(x)\right) = f(u(x)) \quad \text{a.e. in }\Omega \subset \mathbb R^N,NEWLINE\]NEWLINE with the Dirichlet boundary condition. The proofs rely on the Lax-Milgram theorem and on the Schauder fixed point theorem.