Abstract
By using the method of monotone operators, a theorem on the existence of the solution with a special property is obtained for an elliptic variational inequality with discontinuous semimonotone operator; this theorem is then used to prove the existence of a semicorrect solution of a variational inequality with a differential semilinear high-order operator of elliptic type with a nonsymmetric linear part and discontinuous nonlinearity.
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References
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 443–447, March, 1993.
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Pavlenko, V.N. On solvability of variational inequalities with discontinuous semimonotone operators. Ukr Math J 45, 475–480 (1993). https://doi.org/10.1007/BF01061022
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DOI: https://doi.org/10.1007/BF01061022