Remarks on the existence, uniqueness and semi-explicit solvability of systems of autonomous partial differential equations in divergence form with constant boundary conditions

A method is proposed for reducing autonomous nonlinear boundary-value problems of partial differential equations with a particular structure and constant boundary conditions to the simple problem Delta z = 0 in Omega; z = 0 on Gamma(1), z = 1 on Gamma(2), partial derivative z/partial derivative n = 0 on Gamma(3). This requires the solution of a non-standard two-point system of ordinary differential equations. Some applications are also presented for classical problems of mathematical physics.