A variational inequality for the Sturm–Liouville problem with discontinuous nonlinearity

We study a variational inequality for the Sturm–Liouville problem with a nonlinearity that is discontinuous in the phase variable. Previously obtained results for variational inequalities with a spectral parameter and discontinuous operators are applied to this problem. For the variational inequality in the Sturm–Liouville problem with discontinuous nonlinearity, we have established theorems on the existence of semiregular solutions and some bound for the parameter. As an application, we consider the variational inequality for a one-dimensional analog of the Gol'dshtik model for separated flows of an incompressible fluid.