Continuous approximations of discontinuous nonlinearities of semilinear elliptic-type equations
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.
English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 2, pp 249-260.
Citation Example: Iskakov R. S., Pavlenko V. N. Continuous approximations of discontinuous nonlinearities of semilinear elliptic-type equations // Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 224–233.