2019
Том 71
№ 1

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Continuous approximations of discontinuous nonlinearities of semilinear elliptic-type equations

Iskakov R. S., Pavlenko V. N.

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Abstract

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.

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