Continuous approximations of discontinuous nonlinearities of semilinear elliptic-type equations - Iskakov, R. S.; Pavlenko, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We obtain new variational principles of the existence of strong and semiregular solutions of principal boundary-value problems for elliptic-type second-order equations with discontinuous nonlinearity. We study a problem of proximity between the sets of solutions of an approximating problem with nonlinearity continuous in phase variable and solutions of the initial boundary-value problem with discontinuous nonlinearity.