An inverse problem for the compressible Reynolds equation

We study the existence of solutions to a system of equations for equilibrium positions in lubricated journal bearings under load effects. The mechanism under consideration consists of two parallel cylinders, one inside the other, in close distance and relative motion. The unknowns of the problem are the equilibrium position of the inner cylinder and the pressure of the lubricant described by the compressible Reynolds equation. To complete the system, Newton’s second law gives the equilibrium of forces. We present results on existence of solutions for a range of applied forces $ F$.