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Continuous approximations of discontinuous nonlinearities of semilinear elliptic-type equations

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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.

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Authors and Affiliations

  1. Chelyabinsk University, Chelyabinsk

    V. N. Pavlenko & R. S. Iskakov

Authors
  1. V. N. Pavlenko
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  2. R. S. Iskakov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 224–233, February, 1999.

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Pavlenko, V.N., Iskakov, R.S. Continuous approximations of discontinuous nonlinearities of semilinear elliptic-type equations. Ukr Math J 51, 249–260 (1999). https://doi.org/10.1007/BF02513477

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  • DOI: https://doi.org/10.1007/BF02513477

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