Semi-regular solutions of integral equations with discontinuous nonlinearities (Q6636272)

In this paper, integral equations with discontinuous nonlinearities in Lebesgue spaces are considered. Using variational methods, based on the concept of quasipotential operators, a theorem on the existence of semi-regular solutions is established. For equations with one parameter, a theorem on the existence of nontrivial semiregular solutions for sufficiently large parameter values is proved. An interesting example of an applied problem for which the conditions of these theorems are satisfied is given.