Control and perturbation in Sturm — Liouville’s problem with discontinuous nonlinearity

We consider the Sturm — Liouville problem with discontinuous nonlinearity, control and perturbation. Previously obtained results for equations a spectral parameter operator are applied to this problem. By variational method, we have established theorems on existence of solutions nonlinearity optimal problem, as well topological properties set acceptable “control state” pairs. A one-dimensional analog Gol’dshtik model separated flows an incompressible fluid perturbation is given application.