Semi-regular solutions of integral equations with discontinuous nonlinearities

We study integral equations with discontinuous nonlinearities in Lebesgue spaces. Using the variational method, based on the concept of a quasipotential operator, we establish a theorem on the existence of semi-regular solutions. For equations with a parameter, a theorem on the existence of nontrivial semi-regular solutions for sufficiently large parameter values is obtained. An example of an applied problem for which the conditions of these theorems are satisfied is given.